Question 1

A ladder leans against a wall, forming a $$65^\circ$$ angle with the ground. If the foot of the ladder is 5 feet from the wall, how long is the ladder (to the nearest tenth of a foot)?

Accepted Answer

$$11.8 ft$$

Question 2

Given $$\sin 	heta = \dfrac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$-\dfrac{4}{5}$$

Question 3

A Ferris wheel with a radius of $$20$$ meters completes one revolution every $$40$$ seconds. What is the linear speed (in meters per second) of a seat on the edge?

Accepted Answer

$$\dfrac{\pi}{2} m/s$$

Question 4

If the point $$(-3, 4)$$ lies on the terminal side of angle $$	heta in $$standard position, what is $$	an 	heta$$?

Accepted Answer

$$\dfrac{4}{3}$$

Question 5

Given $$\cos 	heta = -0.6$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-0.8$$

Question 6

A point $$P on $$the unit circle has coordinates $$\left(\dfrac{1}{2}, \dfrac{\sqrt{3}}{2}\right). $$What are the coordinates of its reflection across the $$y-$$axis?

Accepted Answer

$$\left(-\dfrac{1}{2}, \dfrac{\sqrt{3}}{2}\right)$$

Question 7

Evaluate $$\sin(2.5)$$ using a calculator (rounded to three decimal places).

Accepted Answer

$$0.598$$

Question 8

Which of the following is the amplitude of the function $$y = -3 \sin(2x) + 1$$?

Accepted Answer

$$3$$

Question 9

What is the period of the function $$y = \cos\left(\dfrac{\pi}{4}x\right)$$?

Accepted Answer

$$8$$

Question 10

A sound wave can be modeled by $$y = 2 \sin(5x). $$What is the maximum value of the wave?

Accepted Answer

$$2$$

Question 11

If $$y = 4 \cos(3x - \dfrac{\pi}{2})$$, what is the phase shift?

Accepted Answer

$$\dfrac{\pi}{6}$$ units\ to\ the\ right$

Question 12

A rotating beacon completes $$15$$ revolutions per minute. What is its angular speed in radians per second?

Accepted Answer

$$1.57$$ rad/s

Question 13

Given $$	an 	heta = -2$$ and $$	heta is in $$Quadrant IV, what is $$\sin 	heta in $$terms of $$\cos 	heta$$?

Accepted Answer

$$-2\cos 	heta$$

Question 14

Which of the following is the correct graph for $$y = \sin(x) + 2$$?

Accepted Answer

A sine wave shifted up by 2 units

Question 15

If $$\sin 	heta = 0.6$$ and $$	heta is in $$Quadrant I, what is $$\cos 	heta$$?

Accepted Answer

$$0.8$$

Question 16

A wheel of radius $$0.5$$ meters rotates at $$120$$ revolutions per minute. What is the linear speed at the rim (in meters per second)?

Accepted Answer

$$2\pi m/s$$

Question 17

Given $$\cos 	heta = 0.3$$ and $$	heta is in $$Quadrant IV, what is $$\sin 	heta$$?

Accepted Answer

$$-0.954$$

Question 18

Which of the following is the correct period for $$y = 2 \sin\left(\dfrac{x}{3}\right)$$?

Accepted Answer

$$6\pi$$

Question 19

If $$y = -2 \cos(x) + 1$$, what is the minimum value of $$y$$?

Accepted Answer

$$-1$$

Unit 1 Study Guide: Trigonometric Functions and Applications

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