How it works
This trig identities quiz has 45 questions in three sets: the reciprocal, quotient and Pythagorean identities, the angle formulas, and expressions to simplify. Each answer comes with the step that proves it.
Read the full guide
Three sets
Basic covers sin²θ + cos²θ = 1 and the two identities you get by dividing it. Angle identities runs from sin(−θ) and cofunctions to the sum, double and power-reducing formulas. Simplify asks you to use them.
Practice or a test
Missed questions come back until you get them right. Print, with a tick on With answer key, gives a paper test for a class. Each wrong choice is a common slip, such as the wrong sign in cos(α + β) or 2 sin θ offered for sin 2θ.
- Learn sin²θ + cos²θ = 1 first: divide it by cos²θ or sin²θ and the other two Pythagorean identities follow.
- For cos(α ± β) the sign between the terms is the opposite of the sign inside.
Questions and answers
What are the basic trig identities?
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, tan²θ + 1 = sec²θ and 1 + cot²θ = csc²θ.
What are the three forms of cos 2θ?
cos²θ − sin²θ, 2cos²θ − 1 and 1 − 2sin²θ. They are the same identity rewritten with sin²θ + cos²θ = 1. Solving the last two for cos²θ and sin²θ gives the power-reducing formulas.
Which trig identities does this quiz leave out?
Product-to-sum and sum-to-product formulas, inverse functions and full proofs. It covers what a precalculus or trigonometry course usually tests first.