Question 1

Given the unit circle, what is the value of $$\sin(\frac{\pi}{4})$$?

Accepted Answer

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

Question 2

Which of the following points lies on the unit circle?

Accepted Answer

$$(1, 0)$$

Question 3

If $$\cos(	heta) = \frac{1}{2}$$ and $$	heta is in $$the first quadrant, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{3}$$

Question 4

A Ferris wheel has a radius of 10 meters. If a seat is at an angle of $$\frac{\pi}{2}$$ radians from the horizontal, what is its height above the center?

Accepted Answer

$$10$$ meters

Question 5

Which equation represents the unit circle?

Accepted Answer

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

Question 6

If $$\sin(	heta) = \frac{\sqrt{3}}{2}$$ and $$	heta is in $$the second quadrant, what is $$	heta$$?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 7

What is the reference angle for $$	heta = \frac{5\pi}{6}$$?

Accepted Answer

$$\frac{\pi}{6}$$

Question 8

If a point on the unit circle has coordinates $$(x, y)$$, what does $$x$$ represent?

Accepted Answer

The cosine of the angle

Question 9

Which of the following is the correct value for $$	an(\frac{\pi}{4})$$?

Accepted Answer

$$1$$

Question 10

A ladder leans against a wall making an angle $$	heta$$ with the ground. If the top of the ladder is 8 meters above the ground and the ladder is 10 meters long, what is $$\sin(	heta)$$?

Accepted Answer

$$0.8$$

Question 11

If $$\cos(	heta) = 0$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values for $$	heta$$?

Accepted Answer

$$\frac{\pi}{2}, \frac{3\pi}{2}$$

Question 12

A point on the unit circle has coordinates $$(-\frac{1}{2}, \frac{\sqrt{3}}{2}). $$What is the corresponding angle in radians?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 13

If $$\sin(	heta) = -1$$, what is $$	heta in $$the interval $$[0, 2\pi)$$?

Accepted Answer

$$\frac{3\pi}{2}$$

Question 14

Which of the following is the period of the sine function?

Accepted Answer

$$2\pi$$

Question 15

If $$	an(	heta) = \sqrt{3}$$ and $$	heta is in $$the first quadrant, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{3}$$

Unit Circle and Graphs of Trigonometric Functions

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