Question 1

Solve for $$x in $$the interval $$0 \leq x \u003c 2\pi if$$ $$\sin 2x = \cos x. $$What is one solution?

Accepted Answer

$$x = \dfrac{\pi}{3}$$

Question 2

Which of the following is equivalent to $$4\cos^2$ x$$?

Accepted Answer

$$8\cos^2$ x - 2$$

Question 3

Evaluate $$\sin(105^\circ)$$ using the sum or difference formula.

Accepted Answer

$$\dfrac{\sqrt{6} + \sqrt{2}}{4}$$

Question 4

If $$\sin \alpha = \dfrac{3}{5}$$ and $$\cos \beta = \dfrac{5}{13}$$ with $$0 \u003c \alpha \u003c \beta \u003c \dfrac{\pi}{2}$$, what is $$\sin(\alpha - \beta)$$?

Accepted Answer

$$-\dfrac{16}{65}$$

Question 5

Which of the following is equivalent to $$\dfrac{\sin^2$ x}{\cos x} + \cos x$$?

Accepted Answer

Question 6

Evaluate $$\arccos\left(	an\left(\dfrac{\pi}{4}ight)ight).$$

Accepted Answer

$$\arccos(1)$$

Question 7

Which of the following is equivalent to $$\sin^2$ x \cos^3$ x$$?

Accepted Answer

$$\sin^2$ x \cos x - \sin^4$ x \cos x$$

Question 8

Solve for $$x in$$ $$0 \leq x \u003c 2\pi if$$ $$2\sec x - 5 = -1.$$

Accepted Answer

$$x = \arccos\left(-\dfrac{1}{3}\right)$$

Question 9

Which of the following is equivalent to $$\dfrac{\sin^2$ x}{\cos x} + \cos x$$?

Accepted Answer

Question 10

Evaluate $$\arcsin\left(\dfrac{\sqrt{3}}{2}\right) in $$the restricted range.

Accepted Answer

$$\dfrac{\pi}{3}$$

Question 11

Which of the following is equivalent to $$\dfrac{\cos^2$ x - 1}{\cos^2$ x}$$ for $$\cos x 
eq 0$$?

Accepted Answer

$$-	an^2$ x$$

Question 12

If $$	an^2$ x + 	an x = 6$$ and $$0 \leq x \u003c 2\pi$$, which of the following is a solution for $$x ($$rounded to three decimals)?

Accepted Answer

$$x \approx 1.040$$

Question 13

Which of the following is equivalent to $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 14

Evaluate $$\sin\left(\arctan\left(-\dfrac{3}{5}\right)\right).$$

Accepted Answer

$$-\dfrac{3}{\sqrt{34}}$$

Question 15

Which of the following is equivalent to $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 16

Which of the following is equivalent to $$\dfrac{1 + \sec x}{\csc x}$$?

Accepted Answer

$$\sin x + 	an x$$

Question 17

Evaluate $$	an\left(\arcsin\left(-\dfrac{5}{6}ight)ight).$$

Accepted Answer

$$-\dfrac{5}{\sqrt{11}}$$

Question 18

Which of the following is equivalent to $$3\sin 2x$$?

Accepted Answer

$$6\sin x \cos x$$

Question 19

Evaluate $$\arctan(-1) in $$the restricted range.

Accepted Answer

$$-\dfrac{\pi}{4}$$

Question 20

Which of the following is equivalent to $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

AP Precalculus Unit 3B Review – Trigonometric Equations, Identities, and Inverse Functions

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