Q: Which of the following is the correct formula for tangent in terms of sine and cosine?

$$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$$

Q: Which of the following is NOT a property of the unit circle?

The coordinates of any point are $$(\sin(\theta), \cos(\theta)).$$

Question 1

On the unit circle, what is the value of $$\sin(90^\circ)$$?

Accepted Answer

$$1$$

Question 2

Which coordinate on the unit circle represents $$\cos(180^\circ)$$?

Accepted Answer

$$x = -1$$

Question 3

If a point on the unit circle is $$(\frac{1}{2}, \frac{\sqrt{3}}{2})$$, what is the angle in degrees?

Accepted Answer

$$30^\circ$$

Question 4

What is the value of $$	an(45^\circ) on $$the unit circle?

Accepted Answer

$$1$$

Question 5

Given the point $$(-\frac{1}{2}, \frac{\sqrt{3}}{2}) on $$the unit circle, what is $$\sin(120^\circ)$$?

Accepted Answer

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

Question 6

Which of the following is the correct formula for tangent in terms of sine and cosine?

Accepted Answer

$$	an(	heta) = \frac{\sin(	heta)}{\cos(	heta)}$$

Question 7

If $$\cos(	heta) = 0$$, which angle $$	heta is $$possible on the unit circle?

Accepted Answer

$$90^\circ$$

Question 8

A point on the unit circle has coordinates $$(0, -1). $$What is the corresponding angle?

Accepted Answer

$$270^\circ$$

Question 9

What is the value of $$\sin(270^\circ)$$?

Accepted Answer

$$-1$$

Question 10

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

Accepted Answer

$$30^\circ$$

Question 11

Which of the following points on the unit circle corresponds to $$225^\circ$$?

Accepted Answer

$$(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2})$$

Question 12

If $$	an(	heta) is $$undefined, which of the following is true?

Accepted Answer

$$\cos(	heta) = 0$$

Question 13

What is the value of $$\cos(0^\circ)$$?

Accepted Answer

$$1$$

Question 14

Which angle has coordinates $$(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}) on $$the unit circle?

Accepted Answer

$$315^\circ$$

Question 15

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

Accepted Answer

$$330^\circ$$

Question 16

A real-world application: If a Ferris wheel makes a full rotation every 60 seconds, what is the sine of the position after 15 seconds, assuming the starting point is at the top?

Accepted Answer

$$\sin(90^\circ) = 1$$

Question 17

Which of the following is NOT a property of the unit circle?

Accepted Answer

The coordinates of any point are $$(\sin(	heta), \cos(	heta)).$$

Question 18

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

Accepted Answer

$$240^\circ$$

Question 19

What is the value of $$	an(180^\circ)$$?

Accepted Answer

$$0$$

Question 20

If a point on the unit circle is $$(0.6, 0.8)$$, what is the value of $$\sin(	heta)$$?

Accepted Answer

$$0.8$$

Trigonometric Functions on the Unit Circle: Sine, Cosine, and Tangent

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