$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$$

$$\sin^2$ \theta + \cos^2$ \theta = 1$$

$$15 \tan 30^\circ = 5\sqrt{3} m$$

$$\sin 2\theta = 2 \sin \theta \cos \theta$$

Question 1

Which of the following is the correct definition of the sine function for an angle $$	heta in a $$right triangle?

Accepted Answer

$$\sin 	heta = \frac{	ext{opposite}}{	ext{hypotenuse}}$$

Question 2

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

Accepted Answer

$$0.8$$

Question 3

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?

Accepted Answer

$$10 \sin 60^\circ = 5\sqrt{3} ft$$

Question 4

Which of the following is the period of the function $$y = 2 \sin(3x)$$?

Accepted Answer

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

Question 5

Given $$	an 	heta = 2$$ and $$	heta is in $$the third quadrant, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{2}{\sqrt{5}}$$

Question 6

A Ferris wheel with a radius of 20 meters makes one complete revolution every 2 minutes. What is the angular velocity in radians per minute?

Accepted Answer

$$\pi$$ radians/minute

Question 7

Which of the following identities is correct?

Accepted Answer

$$\sin^2$ 	heta + \cos^2$ 	heta = 1$$

Question 8

If $$\sin \alpha = 0.5$$ and $$\alpha is in $$the second quadrant, what is $$\cos \alpha$$?

Accepted Answer

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

Question 9

A building casts a 15-meter shadow when the angle of elevation of the sun is $$30^\circ. $$How tall is the building?

Accepted Answer

$$15 	an 30^\circ = 5\sqrt{3} m$$

Question 10

Which of the following is the amplitude of the function $$y = -4 \cos(x)$$?

Accepted Answer

$$4$$

Question 11

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

Accepted Answer

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

Question 12

Which of the following is the correct double angle formula for sine?

Accepted Answer

$$\sin 2	heta = 2 \sin 	heta \cos 	heta$$

Question 13

A ramp rises 3 meters over a horizontal distance of 12 meters. What is the angle of elevation of the ramp?

Accepted Answer

$$\arctan \left( \frac{3}{12} \right)$$

Question 14

Which of the following is the correct value for $$\cos 90^\circ$$?

Accepted Answer

$$0$$

Question 15

If $$	an \alpha = 1$$ and $$\alpha is in $$the fourth quadrant, what is $$\sin \alpha$$?

Accepted Answer

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

Graphs and Functions: Key Concepts and Applications

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