Use the unit circle to determine exact trigonometric values at quadrantal angles and angles with reference angles , , and , apply reciprocal, quotient, Pythagorean, and compound-angle identities, and verify identities while respecting signs, domains, and undefined values. Transform and graph sine, cosine, and tangent functions, interpreting amplitude, period, phase shift, vertical displacement, midline, asymptotes, key features, and standard real-valued models of periodic phenomena. Solve trigonometric equations over specified degree or radian intervals using algebraic manipulation, identities, factoring, substitution, periodicity, quadrant relationships, inverse-trigonometric values, and verification of all solutions.
On this page:
- Master skills like āApply Pythagorean identitiesā, āApply compound-angle identitiesā, and āApply reciprocal and quotient identitiesā with unlimited, free practice problems
- Download (or modify) free worksheets on Trigonometric Functions and Identities you can use at home or in class with practice problems across all skills in this group including āGraph sine, cosine, and tangent functionsā, āVerify fundamental trigonometric identitiesā, āApply transformations to trigonometric functionsā.
- Start working on adaptive units like āFunctions - Sinusoidal - Introā or āFunctions - Transformation, Composition, and Inversion - Practiceā that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Trigonometric Functions and Identities: Individual Skills
Master 9 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Apply Pythagorean identities
- Apply compound-angle identities
- Apply reciprocal and quotient identities
- Apply transformations to trigonometric functions
- Determine amplitude, period, phase shift, and vertical displacement
- Graph sine, cosine, and tangent functions
- Model periodic phenomena with trigonometric functions
- Solve trigonometric equations over specified intervals
- Verify fundamental trigonometric identities
Practice 'Apply Pythagorean identities'
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Download/Modify Free Grade 12 'Trigonometric Functions and Identities' Worksheet
Print this free 'Trigonometric Functions and Identities' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Apply Pythagorean identities
- Apply compound-angle identities
- Apply reciprocal and quotient identities
- Apply transformations to trigonometric functions
- Determine amplitude, period, phase shift, and vertical displacement
- Graph sine, cosine, and tangent functions
- Model periodic phenomena with trigonometric functions
- Solve trigonometric equations over specified intervals
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Trigonometric Functions and Identities) through scaffolded problems that grow in difficulty as concepts are understood.