AP Precalculus – Equivalent Trigonometric Expressions – Drill 1

About This Drill

AP Precalculus – Equivalent Trigonometric Expressions – Drill 1 is a Math practice drill covering Equivalent Trigonometric Expressions. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice rewriting trigonometric expressions using double-angle and Pythagorean identities. These AP® Precalculus questions cover Topic 3.12.

Questions in This Drill

1. Which of the following expressions is equivalent to \( 14\sin(x)\cos(x) \)?
2. Which of the following expressions is equivalent to \( \sin^2(x) + \sin^2(x)\tan^2(x) \)?
3. A student claims that \( \cos(2x) \) and \( 1 - \sin^2(x) \) are equivalent expressions. The table below shows values of each expression at selected inputs.
   
   

   x	cos(2x)	1 − sin²(x)
   0	1	1
   π/6	1/2	3/4
   π/4	0	1/2
   π/3	−1/2	1/4

   
   Based on the table, which of the following best describes the student's claim?
4. A student is solving the equation \( \cos(2\theta) + \cos\theta = 0 \) on \( [0, 2\pi) \). After substituting \( \cos(2\theta) = 2\cos^2\theta - 1 \), the equation becomes \( 2\cos^2\theta + \cos\theta - 1 = 0 \). Which of the following lists all solutions?
5. Which of the following expressions is equivalent to \( \sin^4(x) - \cos^4(x) \), written only in terms of \( \sin(x) \)?