$$\tan x \cdot \sec x = \frac{\sin x}{\cos^2$ x}$$

$$\tan x = \frac{1}{\sqrt{3}}$$

$$\csc x = \frac{1}{\sin x}$$, $$\tan x = \frac{\sin x}{\cos x}$$, $$\sec x = \frac{1}{\cos x}$$

$$(1 + \sin \theta)(1 - \sin \theta)$$

Question 1

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

Accepted Answer

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

Question 2

Given the quotient identity $$	an x = \frac{\sin x}{\cos x}$$, which expression is equivalent to $$\cot x$$?

Accepted Answer

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

Question 3

Which of the following is a Pythagorean identity?

Accepted Answer

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

Question 4

What is the even-odd identity for $$\sin(-x)$$?

Accepted Answer

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

Question 5

If $$	an x = \frac{\sin x}{\cos x}$$ and $$\sec x = \frac{1}{\cos x}$$, what is $$	an x \cdot \sec x in $$terms of $$\sin x$$?

Accepted Answer

$$	an x \cdot \sec x = \frac{\sin x}{\cos^2$ x}$$

Question 6

Which of the following is the correct identity for $$\cos(-x)$$?

Accepted Answer

$$\cos(-x) = \cos x$$

Question 7

Given $$\sin^2$ x + \cos^2$ x = 1$$, what is $$\cos^2$ x in $$terms of $$\sin^2$ x$$?

Accepted Answer

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

Question 8

Which of the following is the correct expression for $$\csc x$$ using reciprocal identities?

Accepted Answer

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

Question 9

If $$\sin x = \frac{1}{2}$$ and $$\cos x = \frac{\sqrt{3}}{2}$$, what is $$	an x$$?

Accepted Answer

$$	an x = \frac{1}{\sqrt{3}}$$

Question 10

Which of the following identities is used to verify $$\csc x \cdot 	an x = \sec x$$?

Accepted Answer

$$\csc x = \frac{1}{\sin x}$$, $$	an x = \frac{\sin x}{\cos x}$$, $$\sec x = \frac{1}{\cos x}$$

Question 11

In the process of verifying the identity $$\frac{\sin x}{1 + \cos x} + \frac{1 + \cos x}{\sin x}$$, what is the least common denominator (LCD)?

Accepted Answer

$$\sin x (1 + \cos x)$$

Question 12

When rewriting $$\frac{1}{1 + \sin 	heta} + \frac{1}{1 - \sin 	heta}$$ with a common denominator, what is the LCD?

Accepted Answer

$$(1 + \sin 	heta)(1 - \sin 	heta)$$

Question 13

If $$\sin^2$ x + \cos^2$ x = 1$$, what is $$\sec^2$ x in $$terms of $$	an^2$ x$$?

Accepted Answer

$$\sec^2$ x = 1 + 	an^2$ x$$

Question 14

Which of the following is the correct even-odd identity for $$	an(-x)$$?

Accepted Answer

$$	an(-x) = -	an x$$

Question 15

If $$\sin x = 0.6$$ and $$\cos x = 0.8$$, what is $$\csc x$$?

Accepted Answer

$$\csc x = \frac{1}{0.6}$$

Question 16

Which of the following is the correct identity for $$\cot x$$ using quotient identities?

Accepted Answer

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

Question 17

If $$\sin x = 0.5$$ and $$\cos x = 0.866$$, what is $$	an x$$?

Accepted Answer

$$	an x = \frac{0.5}{0.866}$$

Question 18

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

Accepted Answer

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

Question 19

If $$\sin x = 0.3$$ and $$\cos x = 0.4$$, what is $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

Verifying Trigonometric Identities: Fundamental Techniques and Examples

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