Question 1

Find the exact value of the expression $$\arcsin\left(\frac{\sqrt{3}}{2}\right). $$Which angle has a sine of $$\frac{\sqrt{3}}{2}$$?

Accepted Answer

$$\frac{\pi}{3}$$

Question 2

Find the inverse function: If $$f(x) = 6\cos(2x)$$, what is $$f^{-1}(1$$)$$?

Accepted Answer

$$\frac{1}{2}\arccos\left(\frac{1}{6}\right)$$

Question 3

Find the exact solution of the equation $$4\cos^2$ x - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{4}, \frac{7\pi}{4}$$

Question 4

Find the exact value of $$\sec$$^{-1}$$(-2).$$

Accepted Answer

$$\frac{2\pi}{3}$$

Question 5

Use a calculator to find the value of $$\sin$$^{-1}$$(0.33) in $$radians, rounded to two decimal places.

Accepted Answer

$$0.34$$

Question 6

Write the trigonometric expression $$\frac{1}{\sin x} in $$terms of its reciprocal identity.

Accepted Answer

$$\csc x$$

Question 7

Solve the equation $$2\sin x = 1 on $$the interval $$[0, 2\pi).$$

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}$$

Question 8

Find the exact value of $$	an\left(\frac{\pi}{4}ight).$$

Accepted Answer

$$1$$

Question 9

Find the exact value of $$\sin\left(\frac{5\pi}{6}\right).$$

Accepted Answer

$$\frac{1}{2}$$

Question 10

Simplify $$2 - \sqrt{3}.$$

Accepted Answer

$$2 - \sqrt{3}$$

Question 11

Use the information that $$\sin x = \frac{3}{5}$$ and $$0 \u003c x \u003c \frac{\pi}{2} to $$find $$	an(2x).$$

Accepted Answer

$$\frac{24}{7}$$

Question 12

If $$	an x = \frac{2}{3}$$ and $$x is in $$Quadrant II, find $$\sin x.$$

Accepted Answer

$$\frac{-2}{\sqrt{13}}$$

Question 13

Express $$\sin(70^\circ)\cos(q) as a $$sum containing only sines or cosines.

Accepted Answer

$$\frac{1}{2}[\sin(70^\circ + q) + \sin(70^\circ - q)]$$

Question 14

Express $$\cos(100^\circ)\cos(50^\circ) as a $$sum or difference of sines and/or cosines.

Accepted Answer

$$\frac{1}{2}[\cos(150^\circ) + \cos(50^\circ)]$$

Trigonometric Functions and Identities: Precalculus Study Guide

Study Guide - Practice Questions