Q: Which of the following statements about the periodicity of trigonometric functions is correct?

$$\sin(\theta + 2\pi) = \sin \theta$$

Question 1

Let $$P = (-3, 4) be a $$point on the terminal side of an angle $$	heta in $$standard position. What is $$\sin 	heta$$?

Accepted Answer

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

Question 2

Which of the following is the domain of the tangent function $$	an 	heta$$?

Accepted Answer

All real numbers except odd integer multiples of $$\frac{\pi}{2}$$

Question 3

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

Accepted Answer

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

Question 4

Which of the following statements about the periodicity of trigonometric functions is correct?

Accepted Answer

$$\sin(	heta + 2\pi) = \sin 	heta$$

Question 5

Given $$	heta = \frac{5\pi}{4}$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 6

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos 	heta$$

Question 7

If $$\cos 	heta = 0$$, which of the following could be a value of $$	heta$$?

Accepted Answer

$$\frac{\pi}{2}$$

Question 8

A Ferris wheel makes one complete revolution every 90 seconds. If the height $$h (in $$meters) of a seat above the ground is modeled by $$h(t) = 10 + 8\sin\left(\frac{2\pi}{90}t\right)$$, what is the period of this function?

Accepted Answer

$$90$$ seconds

Question 9

Which of the following is the range of the cosecant function $$\csc 	heta$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 10

If $$	an 	heta = -1$$ and $$	heta is in $$the fourth quadrant, what is $$	heta$$?

Accepted Answer

$$\frac{7\pi}{4}$$

Question 11

Which of the following is NOT a property of the sine function?

Accepted Answer

Its period is $$\pi.$$

Question 12

If $$\sin 	heta = \frac{3}{5}$$ and $$	heta is in $$the second quadrant, what is $$\cos 	heta$$?

Accepted Answer

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

Question 13

Which of the following best describes the fundamental period of the tangent function?

Accepted Answer

$$\pi$$

Question 14

If $$	heta = 765^\circ$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 45^\circ$$

Question 15

Which of the following is the correct definition of $$\sec 	heta in $$terms of the unit circle?

Accepted Answer

$$\sec 	heta = \frac{1}{a}$$

Question 16

If $$\cot 	heta = 0$$, which of the following could be a value of $$	heta$$?

Accepted Answer

$$\frac{\pi}{2}$$

Question 17

A sound wave can be modeled by $$y = 0.5 \sin(440 \pi t). $$What is the period of this wave?

Accepted Answer

$$\frac{1}{220}$$ seconds

Question 18

Which of the following is true about the cosecant function $$\csc 	heta$$?

Accepted Answer

It is defined for all real numbers except integer multiples of $$\pi.$$

Question 19

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

Accepted Answer

Odd function

Unit Circle Approach and Properties of Trigonometric Functions

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