Question 1

Which of the following best describes a coterminal angle?

Accepted Answer

Two angles that have the same initial side and the same terminal side but different measures.

Question 2

Given the point $$P(5, 4) on $$the terminal side of an angle $$	heta in $$standard position, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{4}{\sqrt{41}}$$

Question 3

Which of the following is the definition of a periodic function?

Accepted Answer

A function $$f$$ such that $$f(t + c) = f(t)$$ for all $$t in $$the domain and some positive number $$c.$$

Question 4

If $$	an 	heta = -\frac{8}{15}$$ and $$	heta is in $$the fourth quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{8}{17}$$

Question 5

Which of the following angles is coterminal with $$60^\circ$$?

Accepted Answer

$$-300^\circ$$

Question 6

A point $$P(x, y)$$ lies on the terminal side of an angle $$	heta in $$standard position. If $$x = -3$$ and $$y = 4$$, what is $$\cos 	heta$$?

Accepted Answer

$$-\frac{3}{5}$$

Question 7

Which of the following statements about the unit circle is true?

Accepted Answer

The unit circle has a radius of $$1$$ and is centered at the origin.

Question 8

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

Accepted Answer

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

Question 9

Which of the following best describes a quadrantal angle?

Accepted Answer

An angle whose terminal side lies along one of the coordinate axes.

Question 10

A Ferris wheel makes one complete revolution every $$40$$ seconds. Which of the following equations best models the height $$h(t) of a $$seat above the ground as a function of time $$t$$, assuming the lowest point is $$2$$ meters above the ground and the radius is $$10$$ meters?

Accepted Answer

$$h(t) = 10 \sin \left( \frac{\pi}{20} t \right) + 12$$

Question 11

If $$t is a $$real number and $$P(x, y) is $$the point on the unit circle corresponding to $$t$$, what is $$\cos t$$?

Accepted Answer

$$x$$

Question 12

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

Accepted Answer

$$2\pi$$

Question 13

If the terminal side of an angle $$	heta in $$standard position passes through the point $$(-8, -15)$$, what is $$	an 	heta$$?

Accepted Answer

$$-\frac{15}{8}$$

Question 14

Which of the following best describes the wrapping function?

Accepted Answer

It associates points on the number line with points on the unit circle using arc length.

Question 15

If $$\cos 	heta = 0$$ and $$	heta is a $$quadrantal angle, what is a possible value for $$	heta$$?

Accepted Answer

$$90^\circ$$

Question 16

A rotating ray starts on the positive $$x-$$axis and rotates $$450^\circ$$ counterclockwise. What is the reference angle?

Accepted Answer

$$90^\circ$$

Trigonometric Functions Extended: Angles, Unit Circle, and Periodicity

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