Question 1

Which of the following is an odd trigonometric function?

Accepted Answer

$$	an(x)$$

Question 2

Given $$\sin(2x) = 2\sin(x)\cos(x)$$, what is $$\sin(2x) if$$ $$\sin(x) = \frac{3}{5}$$ and $$\cos(x) = \frac{4}{5}$$?

Accepted Answer

$$\frac{12}{25}$$

Question 3

Which formula correctly expresses $$\cos(2x) in $$terms of $$\sin(x)$$?

Accepted Answer

$$1 - 2\sin^2$(x)$$

Question 4

A surveyor stands 150 ft from the base of a cliff. The angle of elevation to the top is $$25^\circ. $$What is the height of the cliff to the nearest foot?

Accepted Answer

$$63 ft$$

Question 5

Find all solutions for $$2\cos(x) + \sqrt{3} = 0 in $$the interval $$[0, 2\pi).$$

Accepted Answer

$$x = \frac{5\pi}{6}, \frac{11\pi}{6}$$

Question 6

Convert the polar coordinate $$(3, \frac{\pi}{4}) to $$rectangular form.

Accepted Answer

$$(\frac{3}{\sqrt{2}}, \frac{3}{\sqrt{2}})$$

Question 7

Given $$z_1 = 2$$(\cos 40^\circ + i \sin 40^\circ)$$ and z_2$ = 5(\cos 100^\circ + i \sin 100^\circ)$$, what is $$z_1$$ $$z_2 in $$polar form?

Accepted Answer

$$10(\cos 140^\circ + i \sin 140^\circ)$$

Question 8

Which of the following is the correct sum formula for $$\sin(A+B)$$?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 9

Find the exact value of $$\cos(255^\circ)$$ using the sum or difference formula.

Accepted Answer

$$-\frac{\sqrt{6} + \sqrt{2}}{4}$$

Question 10

Given $$z = 8(\cos 120^\circ + i \sin 120^\circ)$$, what is one fourth root of $$z$$?

Accepted Answer

$$1.68(\cos 30^\circ + i \sin 30^\circ)$$

Question 11

A triangle has sides $$a = 38$$, $$b = 51$$, and $$c = 22. $$Which law should be used to solve for an angle?

Accepted Answer

Law of Cosines

Question 12

Convert the rectangular coordinate $$(-3, 4) to $$polar form.

Accepted Answer

$$(5, 126.87^\circ)$$

Question 13

Find all solutions for $$3\sin(x) + 2 = 0 in $$the interval $$[0, 2\pi).$$

Accepted Answer

$$x = \arcsin(-\frac{2}{3})$$, $$x = \pi - \arcsin(-\frac{2}{3})$$

Question 14

If $$z = 1 - i$$, what is $$z in $$polar form?

Accepted Answer

$$\sqrt{2}(\cos 315^\circ + i \sin 315^\circ)$$

Question 15

Which of the following is the correct half-angle formula for $$\sin\left(\frac{x}{2}\right)$$?

Accepted Answer

$$\sin\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1 - \cos x}{2}}$$

Question 16

A triangle has $$A = 43^\circ$$, $$b = 16$$, $$a = 12. $$Which law should be used to solve for side $$c$$?

Accepted Answer

Law of Sines

Question 17

Evaluate $$\left[2(\cos 45^\circ + i \sin 45^\circ)\right]^3$$ and write the answer in rectangular form.

Accepted Answer

$$-8 + 0i$$

Question 18

Find the exact value of $$\sin(13\pi/12)$$ using the sum or difference formula.

Accepted Answer

$$\frac{\sqrt{6} - \sqrt{2}}{4}$$

Precalculus Study Guide: Trigonometric Identities, Equations, and Complex Numbers

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