Q: Which of the following is the correct definition of $$\csc \theta$$?

$$\csc \theta = \dfrac{1}{\sin \theta}$$

Q: Which of the following is the correct definition of $$\cot \theta$$?

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

Q: Which of the following is the correct definition of $$\tan t$$?

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

Q: Which of the following is equivalent to $$\cot \theta + 1$$?

$$\csc \theta (\cos \theta + \sin \theta)$$

Question 1

Which of the following is the correct fundamental identity relating tangent and secant functions?

Accepted Answer

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

Question 2

If $$\sin^2$ x + 2\sin x + 1 is $$factored, which expression is equivalent?

Accepted Answer

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

Question 3

Which substitution is most helpful when verifying identities involving $$1 + \sin x in $$the denominator?

Accepted Answer

Multiply numerator and denominator by $$1 - \sin x$$

Question 4

Which of the following is the correct definition of $$\csc 	heta$$?

Accepted Answer

$$\csc 	heta = \dfrac{1}{\sin 	heta}$$

Question 5

In electronics, the total energy $$E(t) in a $$radio circuit is given by $$E(t) = k \cos^2$ (2\pi Ft) + k \sin^2$ (2\pi Ft). $$Using trigonometric identities, what is $$E(t)$$?

Accepted Answer

$$E(t) = k$$

Question 6

Which of the following is equivalent to $$\dfrac{\cos x}{1 - \sin x}$$?

Accepted Answer

$$\dfrac{1 + \sin x}{\cos x}$$

Question 7

Which identity is used to simplify $$1 - \sin^2$ x$$?

Accepted Answer

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

Question 8

Which of the following is the correct definition of $$\cot 	heta$$?

Accepted Answer

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

Question 9

Which of the following is the correct definition of $$\sec x$$?

Accepted Answer

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

Question 10

Which of the following is equivalent to $$	an^2$ x (1 + \cot^2$ x)$$?

Accepted Answer

$$\dfrac{1}{1 - \sin^2$ x}$$

Question 11

When verifying trigonometric identities, which strategy is recommended?

Accepted Answer

Work with one side and rewrite it to match the other side

Question 12

Which of the following is equivalent to $$\dfrac{1 + 2\sin \alpha + \sin^2$ \alpha}{\cos^2$ \alpha}$$?

Accepted Answer

$$\dfrac{(1 + \sin \$$alpha)^2$$}{\cos^2$ \alpha}$$

Question 13

Which of the following is equivalent to $$\dfrac{(1 + \sin \$$alpha)^2$$}{1 - \sin^2$ \alpha}$$?

Accepted Answer

$$\dfrac{(1 + \sin \$$alpha)^2$$}{\cos^2$ \alpha}$$

Question 14

Which of the following is the correct definition of $$	an t$$?

Accepted Answer

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

Question 15

Which of the following is equivalent to $$\dfrac{	an t - \cot t}{\sin t \cos t}$$?

Accepted Answer

$$\sec^2$ t - \csc^2$ t$$

Question 16

Which of the following is equivalent to $$\dfrac{1}{\cos^2$ x}$$?

Accepted Answer

$$\sec^2$ x$$

Question 17

Which of the following is equivalent to $$\dfrac{1}{1 - \sin^2$ x}$$?

Accepted Answer

$$\sec^2$ x$$

Question 18

Which of the following is equivalent to $$	an^2$ x + 1$$?

Accepted Answer

$$\sec^2$ x$$

Question 19

Which of the following is equivalent to $$\cot 	heta + 1$$?

Accepted Answer

$$\csc 	heta (\cos 	heta + \sin 	heta)$$

Verifying Trigonometric Identities: Strategies and Applications

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