Q: Which of the following is the correct quotient identity for tangent?

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

Question 1

Which of the following is the equation of the unit circle in the $$xy-$$plane?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 2

Given the point $$P\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) on $$the unit circle, what is $$\cos t$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 3

Which of the following statements is true about the sine and cosine functions?

Accepted Answer

Sine is odd and cosine is even.

Question 4

If $$\sin t = \frac{1}{2}$$ and $$t is in $$the first quadrant, what is $$\cos t$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 5

Which identity is a Pythagorean identity?

Accepted Answer

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

Question 6

If $$	an t = 3$$ and $$\sec t \u003e 0$$, what is $$\sin t$$?

Accepted Answer

$$\frac{3}{\sqrt{10}}$$

Question 7

Which of the following best describes a periodic function?

Accepted Answer

A function that repeats its values at regular intervals.

Question 8

What is the period of the sine function $$f(t) = \sin t$$?

Accepted Answer

$$2\pi$$

Question 9

Evaluate $$\sin\left(\frac{\pi}{4}\right).$$

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 10

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

Accepted Answer

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

Question 11

If $$\sin(-t) = -\sin t$$, what property does the sine function exhibit?

Accepted Answer

Odd function

Question 12

A Ferris wheel makes one complete revolution every $$2\pi$$ minutes. Which trigonometric function best models the height of a seat as a function of time?

Accepted Answer

$$h(t) = a\cos t + b$$

Question 13

If $$\cos t = -\frac{1}{2}$$ and $$t is in $$the third quadrant, what is $$\sin t$$?

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 14

Which of the following is the correct quotient identity for tangent?

Accepted Answer

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

Question 15

If $$\sin t = 0.7071$$, which angle is $$t$$ closest to in radians?

Accepted Answer

$$\frac{\pi}{4}$$

Question 16

Which of the following is the domain of the cosine function?

Accepted Answer

$$(-\infty, \infty)$$

Question 17

If $$	an(-t) = -	an t$$, what does this imply about the tangent function?

Accepted Answer

It is an odd function.

Question 18

A sound wave can be modeled by $$y = \sin t. $$What is the amplitude of this wave?

Accepted Answer

$$1$$

Question 19

If $$\sin t = 0.6$$ and $$\cos t = 0.8$$, what is $$	an t$$?

Accepted Answer

$$0.75$$

Trigonometric Functions: The Unit Circle and Their Properties

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