Q: If $\cos(\theta) = 0$ and $0 \leq \theta < 2\pi$, what are the possible values for $\theta$?

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

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 $0 \leq 	heta < 2\pi$, 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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