Question 1

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

Accepted Answer

$$1$$

Question 2

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

Accepted Answer

$$\sin(	heta)$$

Question 3

What is the equation of the unit circle in the $$xy-$$plane?

Accepted Answer

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

Question 4

Which of the following is the correct value for $$\cos(180^\circ)$$?

Accepted Answer

$$-1$$

Question 5

A ladder leans against a wall making a $$60^\circ$$ angle with the ground. If the ladder is 10 ft long, how high up the wall does it reach? (Use $$\sin(60^\circ) = \sqrt{3}/2)$$

Accepted Answer

$$8.66 ft$$

Question 6

If $$	heta is an $$angle in standard position and its terminal side passes through the point $$(-\frac{1}{2}, \frac{\sqrt{3}}{2})$$, what is $$\cos(	heta)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 7

Which identity is illustrated by the equation $$\sin^2$(	heta) + \cos^2$(	heta) = 1$$?

Accepted Answer

Pythagorean Identity

Question 8

If $$	an(	heta) = \frac{y}{x}$$ for a point $$(x, y) on $$the unit circle, what is $$	an(45^\circ)$$?

Accepted Answer

$$1$$

Question 9

A Ferris wheel has a radius of 20 meters. What is the height above the center when the seat is at an angle of $$30^\circ$$ above the horizontal? (Use $$\sin(30^\circ) = 0.5)$$

Accepted Answer

$$10$$ meters

Question 10

Which of the following is the correct value for $$\sin(270^\circ)$$?

Accepted Answer

$$-1$$

Question 11

If $$\cos(	heta) = 0.6$$ and $$	heta is in $$the first quadrant, what is $$\sin(	heta)$$?

Accepted Answer

$$0.8$$

Question 12

Which of the following points lies on the unit circle?

Accepted Answer

$$(1, 0)$$

Question 13

If $$\sin(	heta) = 0.5$$ and $$	heta is in $$the second quadrant, what is $$	heta$$?

Accepted Answer

$$150^\circ$$

Question 14

A ramp rises 3 meters over a horizontal distance of 5 meters. What is the angle of elevation $$	heta$$? (Use $$\sin(	heta) = \frac{3}{5})$$

Accepted Answer

$$\arcsin(\frac{3}{5})$$

Question 15

If $$\cos(	heta) = -1$$, what is the value of $$	heta in $$degrees?

Accepted Answer

$$180^\circ$$

Solving Systems: Graphical and Algebraic Solutions for Circles and Lines

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