151 Terms and Definitions in Plane and Spherical Trigonometry for the Mathematics Engineering Board Exam

INTRODUCTION

Trigonometry is one of the most consistently tested subjects in the Mathematics engineering licensure examinations. Whether you are reviewing for the ECE, EE, CE, ME, GeE, or any other PRC board exam, you will almost certainly encounter problems that require a solid working knowledge of both plane and spherical trigonometry. The subject shows up not just in the pure mathematics portion of the exam but also bleeds into engineering sciences, surveying, electrical circuit analysis, and signal processing. Ignoring it is simply not an option.

Plane trigonometry deals with the relationships between the sides and angles of triangles drawn on a flat surface. It covers everything from basic angle definitions and the six trigonometric functions to the Laws of Sines and Cosines, trigonometric identities, inverse functions, and wave behavior. These are tools you will use constantly, not just in board exam problems but in your professional practice as an engineer. The board examiners know this, which is why plane trigonometry problems appear in almost every major engineering licensure exam in the country.

Spherical trigonometry extends those same ideas to triangles drawn on the surface of a sphere. This might sound abstract at first, but it has very direct engineering applications in navigation, geodesy, astronomy, and satellite systems. For civil engineers taking the CE board exam, spherical trigonometry connects directly to surveying and geodetic problems. For ECE and EE examinees, it appears in antenna pattern problems and coordinate transformations. Even if only a few items in your exam come from spherical trigonometry, those few items can make the difference between passing and failing. You want to own this topic.

This glossary covers 151 terms drawn from both plane and spherical trigonometry. The terms are arranged alphabetically so you can use this as a quick reference during your review. Each definition is written with the board exam in mind, meaning we explain not just what each term means but why it matters in the context of solving problems under exam conditions. Study these terms carefully, understand the relationships between them, and you will walk into the examination room with confidence.

The 151 Terms and Definitions in Plane and Spherical Trigonometry

1. Acute Angle

An angle whose measure is greater than 0 degrees and less than 90 degrees. In a right triangle, the two non-right angles are always acute. Many trigonometric identities and special angle values used in board exam problems involve acute angles exclusively, so recognizing them quickly saves time during the exam.

2. Acute Triangle

A triangle in which all three interior angles are acute, meaning each angle measures less than 90 degrees. In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides. This relationship is useful when classifying triangles before applying the Law of Cosines.

3. Adjacent Side

In a right triangle, the side that is next to a given acute angle and is not the hypotenuse. The cosine of an angle equals the ratio of the adjacent side to the hypotenuse, and the tangent equals the ratio of the opposite side to the adjacent side. Keeping track of which side is adjacent versus opposite is essential for setting up trigonometric ratios correctly.

4. Altitude (Spherical)

In spherical trigonometry and astronomy, the angular elevation of a celestial body above the horizon, measured along the vertical circle passing through the body. Altitude ranges from 0 degrees at the horizon to 90 degrees at the zenith. It is complementary to the zenith distance. Altitude is one of the unknowns solved for in celestial navigation problems using the astronomical triangle.

5. Ambiguous Case

A situation that arises in the Law of Sines when two sides and a non-included angle are given. Depending on the given measurements, the triangle may have no solution, exactly one solution, or two possible solutions. The ambiguous case is a classic board exam trap. Always check whether the given angle is acute or obtuse and compare the given side opposite the angle to the other given side before concluding how many triangles exist.

6. Amplitude

The maximum displacement of a trigonometric function from its midline or equilibrium position. For a function of the form y = A sin(Bx + C) + D, the amplitude is the absolute value of A. In board exam problems involving waves, oscillations, or AC circuits, the amplitude corresponds to the peak value of the signal. It is always a positive number.

7. Angle

The measure of rotation between two rays sharing a common endpoint called the vertex. Angles can be measured in degrees or radians. In trigonometry, angles can be positive (counterclockwise rotation) or negative (clockwise rotation), which matters when working with angles in standard position on the coordinate plane.

8. Angle of Depression

The angle measured downward from the horizontal line of sight to an object located below the observer. In board exam word problems, the angle of depression is almost always used in combination with right triangle trigonometry to find heights or horizontal distances. Note that the angle of depression from the observer equals the angle of elevation from the object, as they are alternate interior angles.

9. Angle of Elevation

The angle measured upward from the horizontal line of sight to an object located above the observer. Like the angle of depression, it appears frequently in board exam application problems involving towers, buildings, and hills. Always draw a diagram and identify the right triangle before setting up the trigonometric equation.

10. Angle of Inclination

The angle that a line makes with the positive x-axis, measured counterclockwise, ranging from 0 degrees to 180 degrees (exclusive). The tangent of the angle of inclination equals the slope of the line. This concept connects trigonometry directly to analytic geometry and appears in problems involving lines and their orientations on the coordinate plane.

11. Angle Sum of a Spherical Triangle

The sum of the interior angles of a spherical triangle always exceeds 180 degrees and is less than 540 degrees. This is a fundamental distinction between spherical and plane triangles. On a very small spherical triangle, the angle sum approaches 180 degrees and the triangle behaves more like a plane triangle. This property is directly related to the spherical excess and the area of the spherical triangle.

12. Angular Velocity

The rate at which an angle changes with respect to time, typically measured in radians per second. Angular velocity is denoted by the Greek letter omega. In problems involving circular motion or rotating machinery, angular velocity is related to linear velocity by the equation v = rω, where r is the radius of rotation. This term bridges trigonometry with physics and engineering mechanics.

13. Annex Angle

An older term sometimes seen in Mathematics engineering review materials that refers to the supplement of a given angle, or in some contexts, to the reference angle. When you encounter this term in legacy review books, identify the context carefully to determine whether it means 180 minus the angle or the acute reference angle in the appropriate quadrant.

14. Arc

A portion of the circumference of a circle. In trigonometry, arc length is calculated using the formula s = rθ, where r is the radius and θ is the central angle measured in radians. The arc is also foundational in the definition of radian measure itself. Board exam problems frequently ask for arc length given radius and central angle, or for the central angle given arc length and radius.

15. Arc Length Formula

The formula s = rθ, where s is the arc length, r is the radius of the circle, and θ is the central angle in radians. This formula is one of the most frequently used relationships in problems that combine trigonometry with circular motion or geometry. Always convert degrees to radians before applying this formula.

16. Arccosine

The inverse function of cosine, written as arccos(x) or cos⁻¹(x). It returns the angle whose cosine equals x. The range of arccosine is restricted to [0°, 180°] or [0, π] radians to ensure a unique output. In board exam problems, arccos is used to find missing angles when the cosine ratio is known.

17. Arcsine

The inverse function of sine, written as arcsin(x) or sin⁻¹(x). It returns the angle whose sine equals x. The range of arcsine is restricted to [−90°, 90°] or [−π/2, π/2] radians. When solving for angles in right triangle problems, arcsine is used when the ratio of the opposite side to the hypotenuse is known.

18. Arctangent

The inverse function of tangent, written as arctan(x) or tan⁻¹(x). It returns the angle whose tangent equals x. The range of arctangent is restricted to (−90°, 90°) or (−π/2, π/2) radians. Arctangent is commonly used in engineering problems involving slopes, phase angles, and direction angles.

19. Area of a Triangle (Trigonometric Form)

The area of a triangle can be expressed as (1/2)ab sin C, where a and b are two sides of the triangle and C is the included angle between them. This formula is used when the height of the triangle is not directly given. It is derived from the basic area formula and the definition of sine. Board examiners often give two sides and the included angle and ask for the area, making this formula essential.

20. Astronomical Triangle

In spherical trigonometry, the triangle formed on the celestial sphere by the zenith of the observer, the celestial pole, and a celestial body. Its three vertices correspond to three important astronomical reference points. The sides and angles of the astronomical triangle are related to quantities such as altitude, azimuth, hour angle, and declination, all of which appear in navigation and astronomical problems.

21. Azimuth

The horizontal direction of a celestial body or terrestrial point, measured as an angle in the horizontal plane, usually from true north in a clockwise direction. In spherical trigonometry and navigation problems, azimuth appears as one of the unknowns to be solved using the spherical law of sines or cosines. Azimuth problems are common in surveying and geodesy sections of the civil engineering board exam.

22. Bearing

The direction of a line measured as an angle from a reference direction, typically north or south, toward east or west. In board exam problems, bearings appear in two formats: compass bearings (N 30° E) and azimuth bearings (expressed as a single angle from 0° to 360°). Converting between these formats and applying trigonometry to navigation problems is a tested skill.

23. Birectangular Spherical Triangle

A spherical triangle that contains two right angles. In a birectangular spherical triangle, the third angle equals the arc of the opposite side in angular measure. These triangles are a special case studied in spherical trigonometry and help illustrate the differences between spherical and plane geometry. Their properties also serve as instructive examples when exploring Napier’s rules.

24. Celestial Equator

The great circle on the celestial sphere located directly above Earth’s geographic equator. The celestial equator divides the celestial sphere into northern and southern hemispheres. Declination is measured north or south of the celestial equator. In spherical trigonometry problems involving the positions of stars and the sun, the celestial equator serves as the primary reference plane.

25. Celestial Pole

The point on the celestial sphere directly above the geographic north or south pole of Earth. The north celestial pole is located near the star Polaris. In the astronomical triangle, the celestial pole is one of the three vertices. Problems involving latitude determination from star observations use the altitude of the celestial pole, which equals the observer’s geographic latitude.

26. Central Angle

An angle formed at the center of a circle by two radii. The measure of the central angle equals the measure of the arc it intercepts. In trigonometry, the central angle in radians is used in the arc length formula and the sector area formula. Understanding the central angle is foundational for radian measure and circular trigonometry problems.

27. Circumradius

The radius of the circle circumscribed about a triangle, denoted R. By the Law of Sines, the circumradius equals a/(2 sin A) = b/(2 sin B) = c/(2 sin C), where a, b, c are the sides and A, B, C are the opposite angles. The circumradius appears in board exam problems that ask for the radius of the circumscribed circle of a triangle, which is a common geometry-trigonometry hybrid problem.

28. Co-function Identities

A set of identities that relate each trigonometric function to a complementary function. The co-function identities state that sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ, and so on. The prefix “co” in cosine, cotangent, and cosecant literally stands for “complementary.” These identities are used frequently in simplifying expressions and verifying other identities during board exams.

29. Coaxal Circles

A system of circles that share the same radical axis. While this is primarily an advanced geometry concept, it connects to trigonometric applications in problems involving systems of circles and their intersections. This term occasionally appears in advanced Mathematics engineering board exam review materials.

30. Colatitude

The complement of the geographic latitude of a point on Earth’s surface. Colatitude equals 90 degrees minus the latitude. In spherical trigonometry, the colatitude is used in problems involving the celestial sphere and terrestrial navigation because it represents the angular distance from the pole to the point, which is more convenient in many spherical triangle formulations.

31. Complementary Angles

Two angles whose measures add up to 90 degrees. In trigonometry, the sine of an angle equals the cosine of its complement, and the tangent of an angle equals the cotangent of its complement. Recognizing complementary angle pairs allows you to quickly convert between trigonometric functions when simplifying expressions in board exam problems.

32. Complementary Function

In the context of trigonometry and differential equations, the complementary function is the homogeneous solution of a differential equation. While this term has a broader meaning in engineering mathematics, its trigonometric relevance lies in the use of sine and cosine as solutions to second-order linear differential equations with constant coefficients. This connection is critical for electrical engineers dealing with RLC circuits and mechanical engineers dealing with vibrations.

33. Compound Angle

An angle that is expressed as the sum or difference of two simpler angles. The trigonometric functions of compound angles are evaluated using the sum and difference identities. For example, sin(75°) can be computed as sin(45° + 30°) using the sum identity. Recognizing a compound angle and applying the appropriate identity is a frequently tested skill on the engineering board exam.

34. Concyclic Points

Four or more points that all lie on the same circle. In trigonometric and geometric problems, showing that four points are concyclic often involves using the inscribed angle theorem or proving that opposite angles of the formed quadrilateral sum to 180 degrees. This concept appears in problems connecting geometry with trigonometric identities.

35. Cosecant

The reciprocal of the sine function, abbreviated as csc. For an angle θ, csc θ = 1/sin θ = hypotenuse/opposite side. The cosecant function is undefined when sin θ = 0, which occurs at multiples of 180 degrees. In board exam problems, cosecant appears in trigonometric identities and in problems involving reciprocal functions.

36. Cosine

One of the six fundamental trigonometric functions. In a right triangle, cosine of an angle equals the ratio of the adjacent side to the hypotenuse. On the unit circle, cosine corresponds to the x-coordinate of the point on the circle. The cosine function has a range of [−1, 1] and a period of 360 degrees or 2π radians. It is one of the most frequently used functions in all of engineering mathematics.

37. Cosine Rule

See Law of Cosines. The cosine rule is the more commonly used informal name for this law in Mathematics engineering review materials and textbooks.

38. Cotangent

The reciprocal of the tangent function, abbreviated as cot. For an angle θ, cot θ = cos θ/sin θ = adjacent side/opposite side. The cotangent is undefined when sin θ = 0, which occurs at integer multiples of 180 degrees. Cotangent appears frequently in trigonometric identities and in calculus-based engineering problems.

39. Cotangent Rule (Spherical)

Also known as the four-parts formula or the analogue formula for spherical trigonometry. For four consecutive parts of a spherical triangle (two sides and two angles), the formula relates them as: cot a sin b = cos b cos C + sin C cot A. This formula is useful when the given and required parts do not fit neatly into the standard spherical law of sines or cosines configurations.

40. Coterminal Angles

Two or more angles that share the same initial side and the same terminal side when drawn in standard position. Coterminal angles differ by multiples of 360 degrees or 2π radians. For example, 30° and 390° are coterminal. When a given angle is outside the standard range, finding its coterminal angle within [0°, 360°] helps you identify the correct reference angle and quadrant quickly.

41. Coversine

A less common trigonometric function defined as coversine(θ) = 1 − sin θ. Also written as covers(θ). This function appears in older Mathematics engineering board exam review books and in some navigation problems. While rarely seen in modern materials, it is worth recognizing if you encounter it in legacy review resources or historical exam items.

42. Declination

In astronomy and spherical trigonometry, the angular distance of a celestial body north or south of the celestial equator. Declination is analogous to geographic latitude on the celestial sphere. It ranges from −90° (south celestial pole) to +90° (north celestial pole). Problems involving the position of the sun or stars on the celestial sphere require knowledge of declination.

43. Degree

A unit of angle measurement equal to 1/360 of a full rotation. One degree is subdivided into 60 minutes, and one minute is subdivided into 60 seconds. The degree is the most commonly used unit of angle measurement in Mathematics engineering board exam problems, though radians are required in calculus-based problems and formula applications involving arc length and angular velocity.

44. Delambre’s Analogies

An alternative name for Napier’s Analogies in spherical trigonometry. These four formulas relate the half-sums and half-differences of angles and sides in a spherical triangle and are used to check the accuracy of computed solutions. In some Mathematics engineering references, this term appears alongside Napier’s Analogies as an alternative designation for the same set of formulas.

45. Depression Angle

See Angle of Depression. This alternative term appears in some Mathematics review books and engineering references.

46. Difference Identities

Trigonometric identities that express the sine, cosine, or tangent of the difference of two angles in terms of functions of the individual angles. The key formulas are: sin(A − B) = sin A cos B − cos A sin B, cos(A − B) = cos A cos B + sin A sin B, and tan(A − B) = (tan A − tan B)/(1 + tan A tan B). These identities are tested directly in board exams and are also used to derive other identities.

47. Dihedral Angle

The angle between two planes, measured as the angle between lines in each plane that are perpendicular to the common edge. In spherical trigonometry, the angles of a spherical triangle are actually dihedral angles between the planes of the great circles forming the sides. Understanding that spherical triangle angles are dihedral angles helps explain why they can be larger than 90 degrees individually and why their sum exceeds 180 degrees.

48. Double Angle Identities

Identities that express trigonometric functions of twice an angle in terms of functions of the original angle. The most important are: sin(2θ) = 2 sin θ cos θ, cos(2θ) = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ, and tan(2θ) = 2 tan θ/(1 − tan²θ). These identities appear constantly in board exam problems involving simplification, equation solving, and integration.

49. Elevation Angle

See Angle of Elevation.

50. Equilateral Triangle

A triangle in which all three sides are equal in length and all three angles measure exactly 60 degrees. Trigonometric problems involving equilateral triangles often use the fact that splitting one in half produces two 30-60-90 right triangles. Recognizing this allows you to solve for side lengths and heights quickly without using the Law of Cosines.

51. Even Function

A function f(x) for which f(−x) = f(x) for all x in its domain. Among the six trigonometric functions, cosine and secant are even functions. Knowing this property means that cos(−θ) = cos θ, which is useful in simplifying expressions involving negative angles in board exam problems.

52. Excircle

A circle that is tangent to one side of a triangle and to the extensions of the other two sides. A triangle has three excircles. The radius of an excircle (exradius) is denoted r₁, r₂, or r₃. Formulas for exradii are tested in some Mathematics engineering board exams as part of advanced triangle geometry. The exradius formula r₁ = Area/(s − a), where s is the semi-perimeter, is the most commonly tested form.

53. Exsecant

A less common trigonometric function defined as exsecant(θ) = sec θ − 1. It appears in older engineering references, particularly in highway curve problems and some navigation applications. Like coversine, it is not commonly tested in modern board exams but may appear in legacy review materials.

54. Frequency

The number of complete cycles of a periodic function per unit of time or per unit of the independent variable. For a function of the form y = A sin(Bx), the frequency is B/(2π) cycles per unit. In engineering problems involving alternating current, vibrations, and waves, frequency is one of the primary parameters describing the behavior of the system.

55. Fundamental Identities

The set of basic trigonometric identities from which all other identities can be derived. These include the reciprocal identities (csc = 1/sin, sec = 1/cos, cot = 1/tan), the quotient identities (tan = sin/cos, cot = cos/sin), and the Pythagorean identities (sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ). Mastering these fundamental identities is the foundation of success in all trigonometry board exam problems.

56. Geodesic

The shortest path between two points on the surface of a sphere. On a sphere, geodesics are arcs of great circles. In navigation and surveying, the geodesic distance between two points on Earth is calculated using spherical trigonometry formulas. For the civil engineering board exam, understanding that the shortest route between two cities on Earth follows a great circle arc is an important conceptual point.

57. Grade (Angle Measurement)

A unit of angle measurement where a full circle is divided into 400 grades (also called gradians or gons). One grade equals 0.9 degrees and one right angle equals 100 grades. While degrees and radians are far more common in Mathematics board exams, grades appear occasionally in older problems and international references. Knowing how to convert between grades, degrees, and radians is a useful skill.

58. Great Circle

A circle formed on the surface of a sphere by the intersection of the sphere with a plane that passes through the center of the sphere. Great circles are the largest possible circles on a sphere. The equator and all lines of longitude are great circles on Earth. In spherical trigonometry, the sides of a spherical triangle are arcs of great circles. Distances along great circles give the shortest path between two points on a sphere.

59. Great Circle Distance

The shortest distance between two points on the surface of a sphere, measured along the arc of the great circle connecting them. It is calculated using the spherical law of cosines for sides: cos c = cos a cos b + sin a sin b cos C. In navigation problems, the great circle distance between two cities is the actual shortest flight or sailing path, and calculating it is a direct application of spherical trigonometry.

60. Half Angle Identities

Identities that express trigonometric functions of half an angle in terms of functions of the original angle. The key formulas are: sin(θ/2) = ±√[(1 − cos θ)/2], cos(θ/2) = ±√[(1 + cos θ)/2], and tan(θ/2) = (1 − cos θ)/sin θ = sin θ/(1 + cos θ). The sign depends on the quadrant of θ/2. These identities are tested in board exams and are essential in integral calculus problems involving trigonometric substitution.

61. Haversine

A trigonometric function defined as haversine(θ) = (1 − cos θ)/2 = sin²(θ/2). The haversine formula is used in navigation to calculate great circle distances between two points on the surface of a sphere given their latitudes and longitudes. While not commonly tested by name in modern Mathematics board exams, understanding its connection to the half-angle identity for cosine is conceptually valuable.

62. Haversine Formula

A specific application formula used in navigation to compute the great circle distance between two points on a sphere given their latitudes and longitudes. The formula uses the haversine function: hav(d) = hav(φ₂ − φ₁) + cos φ₁ cos φ₂ hav(λ₂ − λ₁), where φ is latitude and λ is longitude. This formula avoids numerical errors that arise with the cosine formula when distances are small and is used in GPS and navigation systems.

63. Heaviside Condition

While primarily a concept in signal processing, this term occasionally appears in older trigonometric references in the context of piecewise sinusoidal functions. In the context of board exam review, focus on recognizing that different trigonometric expressions may apply over different intervals of the independent variable.

64. Hour Angle

In astronomy and spherical trigonometry, the angular distance of a celestial body west of the observer’s meridian, measured along the celestial equator. The hour angle increases at a rate of 15 degrees per hour as Earth rotates. Hour angle problems appear in navigation and geodesy portions of engineering board exams, particularly for civil engineers dealing with astronomical observations for surveying.

65. Hypotenuse

The side of a right triangle that is opposite the right angle. It is always the longest side of the right triangle. The hypotenuse is the denominator in the definitions of sine (opposite/hypotenuse) and cosine (adjacent/hypotenuse). In board exam problems, identifying the hypotenuse is the first step in setting up any right triangle trigonometry problem.

66. Identity

An equation involving trigonometric functions that is true for all values of the variable for which both sides of the equation are defined. Unlike a conditional equation, an identity holds universally. Proving and applying trigonometric identities is a core skill tested in the PRC board exams. The strategy for proving identities is to work on one side only and transform it into the form of the other side.

67. Included Angle

The angle formed between two given sides of a triangle. In the Law of Cosines, the formula c² = a² + b² − 2ab cos C uses C as the included angle between sides a and b. When two sides and the included angle are given, the Law of Cosines is the correct tool to use for finding the third side. This configuration (SAS) does not produce the ambiguous case.

68. Initial Side

The fixed starting ray of an angle in standard position, located along the positive x-axis. The angle is measured from the initial side to the terminal side. Understanding standard position and the initial side is fundamental to working with angles in all four quadrants and with negative angles on the coordinate plane.

69. Inradius

The radius of the circle inscribed within a triangle, denoted r. The inradius is given by r = Area/s, where s is the semi-perimeter of the triangle. It is also expressed as r = (s − a) tan(A/2) = (s − b) tan(B/2) = (s − c) tan(C/2). The inradius appears in board exam problems asking for the radius of the inscribed circle, which is a common combined trigonometry-geometry problem type.

70. Inscribed Angle

An angle formed by two chords of a circle that share an endpoint on the circle. The inscribed angle theorem states that the inscribed angle is exactly half the central angle that subtends the same arc. While this is primarily a geometry concept, it connects to trigonometry in circle theorems and in problems involving cyclic quadrilaterals and triangle circumscription.

151. Zenith Distance

The angular distance from the zenith to a celestial body, measured along the vertical circle through the body. Zenith distance equals 90 degrees minus the altitude (elevation angle above the horizon). In astronomy and navigation problems, zenith distance is one of the sides of the astronomical triangle and is used in spherical trigonometry calculations for finding the position of celestial bodies.

CONCLUSION:

Plane and spherical trigonometry together cover a vast range of topics, and it is easy to feel overwhelmed when reviewing them for the board exam. The good news is that a relatively small number of core concepts and formulas account for the majority of exam items. In plane trigonometry, prioritize the six trigonometric functions and their definitions, the Pythagorean identities, the sum and difference identities, the double angle identities, and the Laws of Sines and Cosines. If you can apply these fluently, you will be able to solve almost any plane trigonometry problem the board throws at you. Pay special attention to the ambiguous case of the Law of Sines, as this is a well-known source of multiple choice traps in the PRC exams.

For spherical trigonometry, focus on understanding the fundamental differences between a spherical triangle and a plane triangle, particularly the fact that the angles sum to more than 180 degrees. Master the spherical law of cosines for sides and the spherical law of sines, as these handle the majority of oblique spherical triangle problems. For right spherical triangles, Napier’s rules are your most efficient tool, and you should practice applying them until they are second nature. Navigation problems involving great circle distance, azimuth, and latitude-longitude calculations are the most common applications tested on the civil and geodetic engineering board exams, so make sure you can set up and solve these problems confidently.

Finally, do not underestimate the value of understanding trigonometric identities deeply rather than just memorizing them. The board exam is designed to test whether you can recognize which identity applies in a given situation and use it correctly under time pressure. Build your understanding by deriving identities from first principles whenever possible, not just writing them down in a list. The 151 terms in this glossary represent the full vocabulary of plane and spherical trigonometry as it applies to the Mathematics engineering licensure examination. Knowing these terms, understanding their definitions, and practicing problems using them will put you in a strong position for exam day.

For practice problems on all these topics, head over to our Trigonometry Problems and Solutions section here on PinoyBix. Hundreds of solved exam-type questions, complete with step by step solutions, organized by topic so you can drill exactly what you need to work on.

Keep reviewing. You are closer than you think.