$$\tan x = \frac{\sin x}{\cos x}$$

Question 1

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 2

Simplify the expression $$\frac{1 - \cos^2$ x}{\sin x}.$$

Accepted Answer

$$\sin x$$

Question 3

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

Accepted Answer

$$\sin u \cos v + \sin v \cos u$$

Question 4

Given $$\sin 85^\circ \cos 25^\circ - \sin 25^\circ \cos 85^\circ$$, which identity is most useful for simplifying this expression?

Accepted Answer

Sine difference formula

Question 5

Find the exact value of $$\cos(195^\circ).$$

Accepted Answer

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

Question 6

Which of the following is an even-odd identity?

Accepted Answer

$$\sin(-x) = -\sin x$$

Question 7

Express $$	an x in $$terms of $$\sin x$$ and $$\cos x$$ using a quotient identity.

Accepted Answer

$$	an x = \frac{\sin x}{\cos x}$$

Question 8

If $$\alpha is in $$Quadrant III and $$\beta is in $$Quadrant II, which is true about $$\sin(\alpha + \beta)$$?

Accepted Answer

It could be positive or negative depending on the values of $$\alpha$$ and $$\beta.$$

Question 9

Which of the following is the reciprocal identity for $$\sec x$$?

Accepted Answer

$$\sec x = \frac{1}{\cos x}$$

Question 10

Simplify $$\sin^2$ x + \cos^2$ x.$$

Accepted Answer

$$1$$

Question 11

Which formula allows you to find the exact value of $$\sin(75^\circ)$$?

Accepted Answer

$$\sin(45^\circ + 30^\circ) = \sin 45^\circ \cos 30^\circ + \sin 30^\circ \cos 45^\circ$$

Question 12

Rationalize the denominator: $$\frac{1}{1 - \sin x}.$$

Accepted Answer

$$\frac{1 + \sin x}{1 - \sin^2$ x}$$

Question 13

Which of the following is the correct difference formula for $$\cos(u - v)$$?

Accepted Answer

$$\cos u \cos v + \sin u \sin v$$

Question 14

If $$\sin x = \frac{3}{5}$$ and $$x is in $$Quadrant II, what is $$\cos x$$?

Accepted Answer

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

Question 15

Which of the following is NOT a fundamental trigonometric identity?

Accepted Answer

$$\sin x = \frac{1}{	an x}$$

Question 16

Which identity would you use to simplify $$\sin(-x)$$?

Accepted Answer

Even-odd identity

Question 17

If $$	an x = 2$$ and $$x is in $$Quadrant III, what is $$\sin x$$?

Accepted Answer

$$-\frac{2}{\sqrt{5}}$$

Question 18

Which of the following is the correct formula for $$\sin(u - v)$$?

Accepted Answer

$$\sin u \cos v - \sin v \cos u$$

Question 19

Which of the following is a reason to use sum and difference formulas?

Accepted Answer

To find exact trigonometric values of angles other than multiples of $$30^\circ$$ and $$45^\circ$$

Trigonometric Identities: Pythagorean, Sum and Difference Formulas

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