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
trigonometry-angle-applications
Questions: 8
Test Difficulty:
trigonometry-angular-velocity
Questions: 8
Test Difficulty:
Average Time Spent: 2 mins 20 secs
trigonometry-arc-length
Questions: 8
Test Difficulty:
Average Time Spent: 7 mins
trigonometry-area-of-a-sector
Questions: 8
Test Difficulty:
trigonometry-angles
Questions: 4
Test Difficulty:
Average Time Spent: 16 mins
trigonometry-angles-in-different-quadrants
Questions: 2
Test Difficulty:
Average Time Spent: 41 secs
trigonometry-complementary-and-supplementary-angles
Questions: 1
Test Difficulty:
Average Time Spent: 23 secs
trigonometry-coterminal-angles
Questions: 1
Test Difficulty:
Average Time Spent: 33 secs
trigonometry-find-all-angles-in-a-range-given-specific-output
Questions: 7
Test Difficulty:
trigonometry-complex-numbers-polar-form
Questions: 11
Test Difficulty:
trigonometry-complex-numbers
Questions: 11
Test Difficulty:
Average Time Spent: 5 mins
trigonometry-de-moivre-s-theorem-and-finding-roots-of-complex-numbers
Questions: 7
Test Difficulty:
trigonometry-polar-form-of-complex-numbers
Questions: 8
Test Difficulty:
trigonometry-practical-applications
Questions: 8
Test Difficulty:
trigonometry-bearing
Questions: 7
Test Difficulty:
trigonometry-inclined-planes-and-air-navigation
Questions: 7
Test Difficulty:
trigonometry-vectors
Questions: 8
Test Difficulty:
Average Time Spent: 5 mins
trigonometry-sum-difference-and-product-identities
Questions: 8
Test Difficulty:
trigonometry-complete-a-proof-using-sums-differences-or-products-of-sines-and-cosines
Questions: 10
Test Difficulty:
trigonometry-product-of-sines-and-cosines
Questions: 8
Test Difficulty:
Average Time Spent: 21 secs
trigonometry-sum-and-difference-of-sines-and-cosines
Questions: 8
Test Difficulty:
Average Time Spent: 21 secs
trigonometry-triangles
Questions: 5
Test Difficulty:
Average Time Spent: 9 mins
trigonometry-area-of-a-triangle
Questions: 8
Test Difficulty:
Average Time Spent: 10 mins
trigonometry-find-the-area-of-a-triangle-using-trigonometry
Questions: 8
Test Difficulty:
trigonometry-law-of-cosines-and-law-of-sines
Questions: 4
Test Difficulty:
Average Time Spent: 9 mins
trigonometry-ambiguous-triangles
Questions: 4
Test Difficulty:
Average Time Spent: 11 mins
trigonometry-law-of-cosines
Questions: 2
Test Difficulty:
Average Time Spent: 12 mins
trigonometry-law-of-sines
Questions: 2
Test Difficulty:
Average Time Spent: 5 mins
trigonometry-right-triangles
Questions: 7
Test Difficulty:
Average Time Spent: 1 d 17 hrs
trigonometry-30-60-90-triangles
Questions: 3
Test Difficulty:
Average Time Spent: 4 mins
trigonometry-45-45-90-triangles
Questions: 4
Test Difficulty:
Average Time Spent: 17 mins
trigonometry-solving-word-problems-with-trigonometry
Questions: 4
Test Difficulty:
trigonometry-trigonometric-applications
Questions: 7
Test Difficulty:
Average Time Spent: 9 mins
trigonometry-use-special-triangles-to-make-deductions
Questions: 10
Test Difficulty:
trigonometry-similar-triangles
Questions: 1
Test Difficulty:
Average Time Spent: 24 secs
trigonometry-identifying-similar-triangles
Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 16 secs
trigonometry-proportions-in-similar-triangles
Questions: 1
Test Difficulty:
Average Time Spent: 13 secs
trigonometry-solving-triangles
Questions: 4
Test Difficulty:
Average Time Spent: 3 mins
trigonometry-finding-angles
Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 45 secs
trigonometry-finding-sides
Questions: 1
Test Difficulty:
Average Time Spent: 22 secs
trigonometry-trigonometric-equations
Questions: 5
Test Difficulty:
Average Time Spent: 5 mins
trigonometry-solving-trigonometric-equations
Questions: 3
Test Difficulty:
Average Time Spent: 56 mins
trigonometry-finding-trigonometric-roots
Questions: 2
Test Difficulty:
Average Time Spent: 41 secs
trigonometry-quadratic-formula-with-trigonometry
Questions: 2
Test Difficulty:
Average Time Spent: 6 mins
trigonometry-systems-of-trigonometric-equations
Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 58 secs
trigonometry-understanding-trigonometric-equations
Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 0 secs
trigonometry-factoring-trigonometric-equations
Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 37 secs
trigonometry-setting-up-trigonometric-equations
Questions: 6
Test Difficulty:
Average Time Spent: 2 mins 45 secs
trigonometry-trigonometric-functions-and-graphs
Questions: 5
Test Difficulty:
Average Time Spent: 5 mins
trigonometry-trigonometric-functions
Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 56 secs
trigonometry-determine-which-values-of-trigonometric-functions-are-undefined
Questions: 1
Test Difficulty:
trigonometry-graphs-of-inverse-trigonometric-functions
Questions: 8
Test Difficulty:
trigonometry-simplifying-trigonometric-functions
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 47 secs
trigonometry-solve-a-trigonometric-function-by-squaring-both-sides
Questions: 8
Test Difficulty:
trigonometry-trigonometric-functions
Questions: 1
Test Difficulty:
Average Time Spent: 3 mins
trigonometry-understand-the-signs-of-the-6-trigonometric-functions-in-each-quadrant
Questions: 1
Test Difficulty:
trigonometry-trigonometric-graphs
Questions: 2
Test Difficulty:
Average Time Spent: 32 secs
trigonometry-determine-vertical-shifts
Questions: 7
Test Difficulty:
trigonometry-graphing-secant-and-cosecant
Questions: 2
Test Difficulty:
Average Time Spent: 56 secs
trigonometry-graphing-sine-and-cosine
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 12 secs
trigonometry-graphing-tangent-and-cotangent
Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 46 secs
trigonometry-period-and-amplitude
Questions: 2
Test Difficulty:
Average Time Spent: 33 secs
trigonometry-phase-shifts
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 28 secs
trigonometry-trigonometric-identities
Questions: 4
Test Difficulty:
Average Time Spent: 2 mins 27 secs
trigonometry-apply-basic-and-definitional-identities
Questions: 6
Test Difficulty:
Average Time Spent: 12 mins
trigonometry-complementary-and-supplementary-identities
Questions: 2
Test Difficulty:
Average Time Spent: 53 secs
trigonometry-complete-basic-trigonometry-proofs
Questions: 1
Test Difficulty:
trigonometry-identities-of-doubled-angles
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 11 secs
trigonometry-identities-of-halved-angles
Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 54 secs
trigonometry-identities-of-inverse-operations
Questions: 6
Test Difficulty:
Average Time Spent: 5 mins
trigonometry-identities-of-squared-trigonometric-functions
Questions: 3
Test Difficulty:
Average Time Spent: 14 mins
trigonometry-identities-with-angle-sums
Questions: 4
Test Difficulty:
Average Time Spent: 6 mins
trigonometry-pythagorean-identities
Questions: 3
Test Difficulty:
Average Time Spent: 1 mins 44 secs
trigonometry-sum-and-product-identities
Questions: 2
Test Difficulty:
Average Time Spent: 2 mins 5 secs
trigonometry-trigonometric-operations
Questions: 1
Test Difficulty:
Average Time Spent: 1 mins 7 secs
trigonometry-arcsin-arccos-arctan
Questions: 1
Test Difficulty:
Average Time Spent: 2 mins 8 secs
trigonometry-sec-csc-ctan
Questions: 3
Test Difficulty:
Average Time Spent: 2 mins 4 secs
trigonometry-sin-cos-tan
Questions: 2
Test Difficulty:
Average Time Spent: 1 mins 12 secs
trigonometry-unit-circle-and-radians
Questions: 2
Test Difficulty:
Average Time Spent: 45 secs
trigonometry-angles-in-the-unit-circle
Questions: 2
Test Difficulty:
Average Time Spent: 45 secs
trigonometry-radians-and-conversions
Questions: 2
Test Difficulty:
Average Time Spent: 39 secs
trigonometry-unit-circle
Questions: 2
Test Difficulty:
Average Time Spent: 28 secs
All Trigonometry Resources