Q: Which of the following is a correct application of the Pythagorean Identity?

$$\tan^2$ \theta + 1 = \sec^2$ \theta$$

Q: Which of the following is an Even-Odd Identity?

$$\sin(-\theta) = -\sin \theta$$

Q: Rewrite $$\tan \theta in $$terms of sine and cosine.

$$\dfrac{\sin \theta}{\cos \theta}$$

Q: Which of the following is NOT a reciprocal identity?

$$\tan \theta = \dfrac{\sin \theta}{\cos \theta}$$

Q: Which of the following is a valid identity for all values of $$\theta$$ for which both sides are defined?

$$\cot \theta = \dfrac{\cos \theta}{\sin \theta}$$

Q: Which of the following is a correct application of the Even-Odd identities?

$$\tan(-\theta) = -\tan \theta$$

Q: Which of the following is the correct simplification for $$\dfrac{1}{1 - \sin \theta}$$ multiplied by $$\dfrac{1 + \sin \theta}{1 + \sin \theta}$$?

$$\dfrac{1 + \sin \theta}{1 - \sin^2$ \theta}$$

Q: Which of the following is the correct simplification of $$\sin^2$(-\theta) - \cos^2$(-\theta)$$?

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

Q: Which of the following is the correct simplification of $$\tan \theta + \cot \theta in $$terms of sine and cosine?

$$\dfrac{\sin^2$ \theta + \cos^2$ \theta}{\sin \theta \cos \theta}$$

Question 1

Which of the following is a correct application of the Pythagorean Identity?

Accepted Answer

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

Question 2

Simplify the expression $$\dfrac{1}{\sin 	heta}$$ using a reciprocal identity.

Accepted Answer

$$\csc 	heta$$

Question 3

Which of the following is an Even-Odd Identity?

Accepted Answer

$$\sin(-	heta) = -\sin 	heta$$

Question 4

Rewrite $$	an 	heta in $$terms of sine and cosine.

Accepted Answer

$$\dfrac{\sin 	heta}{\cos 	heta}$$

Question 5

Which algebraic technique is used when multiplying numerator and denominator by $$1 + \sin 	heta to $$simplify $$\dfrac{1 - \sin 	heta}{\cos 	heta}$$?

Accepted Answer

Multiplying by a well-chosen 1

Question 6

Which of the following is NOT a reciprocal identity?

Accepted Answer

$$	an 	heta = \dfrac{\sin 	heta}{\cos 	heta}$$

Question 7

Which of the following is the correct simplification of $$\sin^2$ 	heta + \cos^2$ 	heta$$?

Accepted Answer

$$1$$

Question 8

If $$\sin(-	heta) = -\sin 	heta$$, what is $$\cos(-	heta)$$?

Accepted Answer

$$\cos 	heta$$

Question 9

Which of the following is a valid identity for all values of $$	heta$$ for which both sides are defined?

Accepted Answer

$$\cot 	heta = \dfrac{\cos 	heta}{\sin 	heta}$$

Question 10

Which of the following best describes an identity?

Accepted Answer

An equation that is true for all values in the domain of the variable

Question 11

Simplify $$\dfrac{\sin 	heta}{1 + \cos 	heta} + \dfrac{1 + \cos 	heta}{\sin 	heta}$$ and choose the correct answer.

Accepted Answer

$$2 \csc 	heta$$

Question 12

Which of the following is the correct simplification of $$	an^2$ 	heta + 1$$?

Accepted Answer

$$\sec^2$ 	heta$$

Question 13

Which of the following is a correct application of the Even-Odd identities?

Accepted Answer

$$	an(-	heta) = -	an 	heta$$

Question 14

Which of the following is the correct simplification for $$\dfrac{1}{1 - \sin 	heta}$$ multiplied by $$\dfrac{1 + \sin 	heta}{1 + \sin 	heta}$$?

Accepted Answer

$$\dfrac{1 + \sin 	heta}{1 - \sin^2$ 	heta}$$

Question 15

Which of the following is the correct simplification of $$\dfrac{1 - \cos^2$ 	heta}{\sin 	heta}$$?

Accepted Answer

$$\sin 	heta$$

Question 16

Which of the following is the correct simplification of $$\csc 	heta \cdot 	an 	heta$$?

Accepted Answer

$$\sec 	heta$$

Question 17

Which of the following is the correct simplification of $$\sin^2$(-	heta) - \cos^2$(-	heta)$$?

Accepted Answer

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

Question 18

Which of the following is the correct simplification of $$	an 	heta + \cot 	heta in $$terms of sine and cosine?

Accepted Answer

$$\dfrac{\sin^2$ 	heta + \cos^2$ 	heta}{\sin 	heta \cos 	heta}$$

Question 19

Which of the following is the correct simplification of $$\dfrac{1 - \sin 	heta}{\cos 	heta} by $$multiplying numerator and denominator by $$1 + \sin 	heta$$?

Accepted Answer

$$\sec 	heta - 	an 	heta$$

Analytic Trigonometry: Trigonometric Identities and Algebraic Techniques

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