Take the Varsity Learning Tools free diagnostic test for Trigonometry to determine which academic concepts you understand and which ones require your ongoing attention. Each Trigonometry problem is tagged down to the core, underlying concept that is being tested. The Trigonometry diagnostic test results highlight how you performed on each area of the test. You can then utilize the results to create a personalized study plan that is based on your particular area of need.
High school Trigonometry classes introduce students to various trigonometric identities, properties, and functions in detail. Students typically take Trigonometry after completing previous coursework in Algebra and Geometry, but before taking Pre-Calculus and Calculus. Information students learn in Trigonometry helps them succeed in later higher-level mathematics courses, as well as in science courses like Physics, where trigonometric functions are used to model certain physical phenomena.
Like Pre-Algebra, Algebra I, and Algebra II classes, Trigonometry classes focus on functions and graphs. Trigonometry in particular investigates trigonometric functions, and in the process teaches students how to graph sine, cosine, secant, cosecant, tangent, cotangent, arcsin, arccos, and arctan functions, as well as how to perform phase shifts and calculate their periods and amplitudes. Trigonometric operations are also discussed, and students also learn about trigonometric equations, including how to understand, set up, and factor trig equations, how to solve individual trigonometric equations, as well as systems of trigonometric equations, how to find trig roots, and how to use the quadratic formula on trigonometric equations.
Trigonometric identities are also discussed in Trigonometry classes; students learn about the sum and product identities, as well as identities of inverse operations, squared trigonometric functions, halved angles, and doubled angles. Students also learn to work with identities with angle sums, complementary and supplementary identities, pythagorean identities, and basic and definitional identities.
Another major part of Trigonometry is learning to analyze specific kinds of special triangles. Students learn to determine angles and side lengths in 30-60-90 and 45-45-90 right triangles using the law of sines and the law of cosines, as well as how to identify similar triangles and determine proportions using proportionality.
Trigonometry also teaches students about the unit circles and radians, focusing on how to convert degrees into radians and vice versa. Complementary, supplementary, and coterminal angles are all discussed. This focus on angles in the unit circle is also applied to the coordinate plane when angles in different quadrants are examined.
As may now be apparent, many students find themselves very apprehensive about taking, and keeping up with, a Trigonometry course. Resources like Varsity Tutors’ free Trigonometry Practice Tests can help them channel any nervousness they feel about the course into a process of active review that will benefit them. Each Trigonometry Practice Test features a dozen multiple-choice Trigonometry questions, and each question comes with a full step-by-step explanation to help students who miss it learn the concepts being tested. Questions are organized in Practice Tests, which draw from various topics taught in Trigonometry; questions are also organized by concept. So, if a student wants to focus on only answering questions about using the law of sines, questions organized by concept makes this possible. Using Varsity Tutors’ free Trigonometry Practice Tests, students can practice material they find difficult and reduce apprehension they may feel about Trigonometry.
Our completely free Trigonometry practice tests are the perfect way to brush up your skills. Take one of our many Trigonometry practice tests for a run-through of commonly asked questions. You will receive incredibly detailed scoring results at the end of your Trigonometry practice test to help you identify your strengths and weaknesses. Pick one of our Trigonometry practice tests now and begin!
Practice Tests by Concept
Angle applications practice test
trigonometry-angle-applications
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Questions: 8
Test Difficulty:
Average Time Spent: 2 mins 39 secs
Angular velocity practice test
trigonometry-angular-velocity
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Questions: 8
Test Difficulty:
Average Time Spent: 2 mins 24 secs
Arc length practice test
trigonometry-arc-length
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Questions: 8
Test Difficulty:
Average Time Spent: 5 mins
Area of a sector practice test
trigonometry-area-of-a-sector
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Questions: 8
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Angles practice test
trigonometry-angles
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Questions: 4
Test Difficulty:
Average Time Spent: 16 mins
Angles in different quadrants practice test
trigonometry-angles-in-different-quadrants
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Questions: 2
Test Difficulty:
Average Time Spent: 41 secs
Complementary and supplementary angles practice test
trigonometry-complementary-and-supplementary-angles
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Questions: 1
Test Difficulty:
Average Time Spent: 23 secs
Coterminal angles practice test
trigonometry-coterminal-angles
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Questions: 1
Test Difficulty:
Average Time Spent: 33 secs
Find all angles in a range given specific output practice test
trigonometry-find-all-angles-in-a-range-given-specific-output
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Questions: 7
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Complex numbers/polar form practice test
trigonometry-complex-numbers-polar-form
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Questions: 11
Test Difficulty:
Average Time Spent: 5 mins
Complex numbers practice test
trigonometry-complex-numbers
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Questions: 11
Test Difficulty:
Average Time Spent: 4 mins
De moivre's theorem and finding roots of complex numbers practice test
trigonometry-de-moivre-s-theorem-and-finding-roots-of-complex-numbers
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Questions: 7
Test Difficulty:
Average Time Spent: 7 mins
Polar form of complex numbers practice test
trigonometry-polar-form-of-complex-numbers
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Questions: 8
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Practical applications practice test
trigonometry-practical-applications
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Questions: 8
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Bearing practice test
trigonometry-bearing
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Questions: 7
Test Difficulty:
Average Time Spent: 2 mins 55 secs
Inclined planes and air navigation practice test
trigonometry-inclined-planes-and-air-navigation
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Questions: 7
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Vectors practice test
trigonometry-vectors
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Questions: 8
Test Difficulty:
Average Time Spent: 2 mins 44 secs
Sum, difference, and product identities practice test
trigonometry-sum-difference-and-product-identities
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Questions: 8
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Complete a proof using sums, differences, or products of sines and cosines practice test
trigonometry-complete-a-proof-using-sums-differences-or-products-of-sines-and-cosines
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Questions: 10
Test Difficulty:
Average Time Spent: 2 mins 52 secs
Product of sines and cosines practice test
trigonometry-product-of-sines-and-cosines
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Questions: 8
Test Difficulty:
Average Time Spent: 4 mins
Sum and difference of sines and cosines practice test
trigonometry-sum-and-difference-of-sines-and-cosines
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Questions: 8
Test Difficulty:
Average Time Spent: 6 mins
Triangles practice test
trigonometry-triangles
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Questions: 5
Test Difficulty:
Average Time Spent: 9 mins
Area of a triangle practice test
trigonometry-area-of-a-triangle
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Questions: 8
Test Difficulty:
Average Time Spent: 6 mins
Find the area of a triangle using trigonometry practice test
trigonometry-find-the-area-of-a-triangle-using-trigonometry
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Questions: 8
Test Difficulty:
Law of cosines and law of sines practice test
trigonometry-law-of-cosines-and-law-of-sines
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Questions: 4
Test Difficulty:
Average Time Spent: 4 mins
Ambiguous triangles practice test
trigonometry-ambiguous-triangles
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Questions: 4
Test Difficulty:
Average Time Spent: 6 mins
Law of cosines practice test
trigonometry-law-of-cosines
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Questions: 2
Test Difficulty:
Average Time Spent: 7 mins
Law of sines practice test
trigonometry-law-of-sines
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Questions: 2
Test Difficulty:
Average Time Spent: 5 mins
Right triangles practice test
trigonometry-right-triangles
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Questions: 7
Test Difficulty:
Average Time Spent: 5 mins
30-60-90 triangles practice test
trigonometry-30-60-90-triangles
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Questions: 3
Test Difficulty:
Average Time Spent: 4 mins
45-45-90 triangles practice test
trigonometry-45-45-90-triangles
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Questions: 4
Test Difficulty:
Average Time Spent: 17 mins
Solving word problems with trigonometry practice test
trigonometry-solving-word-problems-with-trigonometry
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Questions: 4
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Trigonometric applications practice test
trigonometry-trigonometric-applications
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Questions: 7
Test Difficulty:
Average Time Spent: 7 mins
Use special triangles to make deductions practice test
trigonometry-use-special-triangles-to-make-deductions
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Questions: 10
Test Difficulty:
Average Time Spent: 1 hrs 45 mins
Similar triangles practice test
trigonometry-similar-triangles
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Questions: 1
Test Difficulty:
Average Time Spent: 24 secs
Identifying similar triangles practice test
trigonometry-identifying-similar-triangles
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Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 16 secs
Proportions in similar triangles practice test
trigonometry-proportions-in-similar-triangles
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Questions: 1
Test Difficulty:
Average Time Spent: 13 secs
Solving triangles practice test
trigonometry-solving-triangles
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Questions: 4
Test Difficulty:
Average Time Spent: 3 mins
Finding angles practice test
trigonometry-finding-angles
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Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 45 secs
Finding sides practice test
trigonometry-finding-sides
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Questions: 1
Test Difficulty:
Average Time Spent: 36 secs
Trigonometric equations practice test
trigonometry-trigonometric-equations
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Questions: 5
Test Difficulty:
Average Time Spent: 5 mins
Solving trigonometric equations practice test
trigonometry-solving-trigonometric-equations
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Questions: 3
Test Difficulty:
Average Time Spent: 46 mins
Finding trigonometric roots practice test
trigonometry-finding-trigonometric-roots
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Questions: 2
Test Difficulty:
Average Time Spent: 38 mins
Quadratic formula with trigonometry practice test
trigonometry-quadratic-formula-with-trigonometry
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Questions: 2
Test Difficulty:
Average Time Spent: 45 mins
Systems of trigonometric equations practice test
trigonometry-systems-of-trigonometric-equations
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Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 58 secs
Understanding trigonometric equations practice test
trigonometry-understanding-trigonometric-equations
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Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 0 secs
Factoring trigonometric equations practice test
trigonometry-factoring-trigonometric-equations
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Questions: 2
Test Difficulty:
Average Time Spent: 53 secs
Setting up trigonometric equations practice test
trigonometry-setting-up-trigonometric-equations
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Questions: 6
Test Difficulty:
Average Time Spent: 2 mins 53 secs
Trigonometric functions and graphs practice test
trigonometry-trigonometric-functions-and-graphs
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Questions: 5
Test Difficulty:
Average Time Spent: 5 mins
Trigonometric functions practice test
trigonometry-trigonometric-functions
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Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 56 secs
Determine which values of trigonometric functions are undefined practice test
trigonometry-determine-which-values-of-trigonometric-functions-are-undefined
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Questions: 1
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Graphs of inverse trigonometric functions practice test
trigonometry-graphs-of-inverse-trigonometric-functions
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Questions: 8
Test Difficulty:
Average Time Spent: 2 mins 38 secs
Simplifying trigonometric functions practice test
trigonometry-simplifying-trigonometric-functions
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Questions: 2
Test Difficulty:
Average Time Spent: 24 mins
Solve a trigonometric function by squaring both sides practice test
trigonometry-solve-a-trigonometric-function-by-squaring-both-sides
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Questions: 8
Test Difficulty:
Trigonometric functions practice test
trigonometry-trigonometric-functions
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Questions: 1
Test Difficulty:
Average Time Spent: 3 mins
Understand the signs of the 6 trigonometric functions in each quadrant practice test
trigonometry-understand-the-signs-of-the-6-trigonometric-functions-in-each-quadrant
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Questions: 1
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Trigonometric graphs practice test
trigonometry-trigonometric-graphs
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Questions: 2
Test Difficulty:
Average Time Spent: 32 secs
Determine vertical shifts practice test
trigonometry-determine-vertical-shifts
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Questions: 7
Test Difficulty:
Average Time Spent: 2 mins 44 secs
Graphing secant and cosecant practice test
trigonometry-graphing-secant-and-cosecant
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Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 1 secs
Graphing sine and cosine practice test
trigonometry-graphing-sine-and-cosine
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Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 11 secs
Graphing tangent and cotangent practice test
trigonometry-graphing-tangent-and-cotangent
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Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 53 secs
Period and amplitude practice test
trigonometry-period-and-amplitude
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Questions: 2
Test Difficulty:
Average Time Spent: 33 secs
Phase shifts practice test
trigonometry-phase-shifts
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Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 28 secs
Trigonometric identities practice test
trigonometry-trigonometric-identities
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Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 27 secs
Apply basic and definitional identities practice test
trigonometry-apply-basic-and-definitional-identities
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Questions: 6
Test Difficulty:
Average Time Spent: 3 mins
Complementary and supplementary identities practice test
trigonometry-complementary-and-supplementary-identities
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Questions: 2
Test Difficulty:
Average Time Spent: 51 secs
Complete basic trigonometry proofs practice test
trigonometry-complete-basic-trigonometry-proofs
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Questions: 1
Test Difficulty:
Average Time Spent: 21 secs
Identities of doubled angles practice test
trigonometry-identities-of-doubled-angles
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Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 11 secs
Identities of halved angles practice test
trigonometry-identities-of-halved-angles
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Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 54 secs
Identities of inverse operations practice test
trigonometry-identities-of-inverse-operations
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Questions: 6
Test Difficulty:
Average Time Spent: 16 mins
Identities of squared trigonometric functions practice test
trigonometry-identities-of-squared-trigonometric-functions
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Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 31 secs
Identities with angle sums practice test
trigonometry-identities-with-angle-sums
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Questions: 4
Test Difficulty:
Average Time Spent: 4 mins
Pythagorean identities practice test
trigonometry-pythagorean-identities
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Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 44 secs
Sum and product identities practice test
trigonometry-sum-and-product-identities
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Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 5 secs
Trigonometric operations practice test
trigonometry-trigonometric-operations
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Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 2 secs
Arcsin, arccos, arctan practice test
trigonometry-arcsin-arccos-arctan
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Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 8 secs
Sec, csc, ctan practice test
trigonometry-sec-csc-ctan
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Questions: 3
Test Difficulty:
Average Time Spent: 10 mins
Sin, cos, tan practice test
trigonometry-sin-cos-tan
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Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 6 secs
Unit circle and radians practice test
trigonometry-unit-circle-and-radians
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Questions: 2
Test Difficulty:
Average Time Spent: 45 secs
Angles in the unit circle practice test
trigonometry-angles-in-the-unit-circle
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Questions: 2
Test Difficulty:
Average Time Spent: 44 secs
Radians and conversions practice test
trigonometry-radians-and-conversions
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Questions: 2
Test Difficulty:
Average Time Spent: 40 secs
Unit circle practice test
trigonometry-unit-circle
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Questions: 2
Test Difficulty:
Average Time Spent: 28 secs
All Trigonometry Resources
6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept
