Q: Which of the following is the correct formula for the range $$R of a $$projectile launched at an angle $$\theta$$ with initial velocity $$v_0 ($$ignoring air resistance)?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Q: Which of the following is the correct sum formula for $$\tan(\alpha + \beta)$$?

$$\tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$$

Q: Which of the following is the correct double-angle formula for $$\cos 2\theta$$?

$$\cos 2\theta = \cos^2$ \theta - \sin^2$ \theta$$

Question 1

Which of the following is the correct domain and range for the inverse sine function $$y = \sin$$^{-1}$$ x$$?

Accepted Answer

Domain: $$[-1, 1]$$, Range: \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right]$

Question 2

Find the exact value of $$\sin$$^{-1}$$\left( -1 \right).$$

Accepted Answer

$$-\frac{\pi}{2}$$

Question 3

Evaluate $$\cos\left( \sin$$^{-1}$$\left( \frac{3}{5} \right) \right).$$

Accepted Answer

$$\frac{4}{5}$$

Question 4

Which of the following is the correct formula for the range $$R of a $$projectile launched at an angle $$	heta$$ with initial velocity $$v_0 ($$ignoring air resistance)?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 5

If $$	an \alpha = -2$$ and $$\alpha is in $$quadrant II, what is $$\sin 2\alpha$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 6

Which of the following is an identity?

Accepted Answer

$$\sin^2$ x + \cos^2$ x = 1$$

Question 7

Express $$\sin x \cos y as a $$sum using a product-to-sum formula.

Accepted Answer

$$\frac{1}{2} [\sin(x+y) + \sin(x-y)]$$

Question 8

Solve for $$x in$$ $$2\sin x - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

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

Question 9

Which of the following is the correct half-angle formula for $$\sin \frac{\alpha}{2}$$?

Accepted Answer

$$\sin \frac{\alpha}{2} = \pm \sqrt{\frac{1 - \cos \alpha}{2}}$$

Question 10

If $$\sin 	heta = -\frac{3}{5}$$ and $$	heta is in $$quadrant IV, what is $$\cos 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 11

Which of the following is the correct sum formula for $$	an(\alpha + \beta)$$?

Accepted Answer

$$	an(\alpha + \beta) = \frac{	an \alpha + 	an \beta}{1 - 	an \alpha 	an \beta}$$

Question 12

Find the exact value of $$\cos$$^{-1}$$\left( -1 \right).$$

Accepted Answer

$$\pi$$

Question 13

Which of the following is the correct expression for $$\sin(\alpha - \beta)$$?

Accepted Answer

$$\sin \alpha \cos \beta - \cos \alpha \sin \beta$$

Question 14

If $$\sin \alpha = \frac{5}{13}$$ and $$\alpha is in $$quadrant II, what is $$\cos \alpha$$?

Accepted Answer

$$-\frac{12}{13}$$

Question 15

Which of the following is the correct double-angle formula for $$\cos 2	heta$$?

Accepted Answer

$$\cos 2	heta = \cos^2$ 	heta - \sin^2$ 	heta$$

Question 16

Solve for $$x in$$ $$	an x = 1$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \frac{\pi}{4}, \frac{5\pi}{4}$$

Question 17

Which of the following is the correct sum-to-product formula for $$\sin x + \sin y$$?

Accepted Answer

$$2 \sin \left( \frac{x+y}{2} \right) \cos \left( \frac{x-y}{2} \right)$$

Analytic Trigonometry: Inverse Functions, Equations, and Identities

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