Question 1

A Ferris wheel with a radius of 20 meters completes one full revolution every 2 minutes. What is the linear speed (in meters per minute) of a seat on the edge of the wheel?

Accepted Answer

$$40\pi$$

Question 2

Convert $$135^{\circ} to $$radians.

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

$$3$$

Question 5

Find the exact value of $$\sin(75$$^{\circ}$$)$$ using sum and difference formulas.

Accepted Answer

$$\dfrac{\sqrt{6} + \sqrt{2}}{4}$$

Question 6

A ladder leans against a wall, forming 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 7

Which of the following is an even trigonometric function?

Accepted Answer

$$\cos(x)$$

Question 8

Solve for $$x in$$ $$2\sin^2$(x) - 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \dfrac{\pi}{2}, \dfrac{3\pi}{2}$$

Question 9

Given $$	an(\alpha) = 2$$ and $$\alpha is in $$Quadrant III, what is $$\sin(\alpha)$$?

Accepted Answer

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

Question 10

Which equation represents a sine function with amplitude 4, period $$\pi$$, and phase shift $$\dfrac{\pi}{4} to $$the right?

Accepted Answer

$$y = 4\sin(2x - \dfrac{\pi}{2})$$

Question 11

If $$\vec{v} = \langle 3, 4 \rangle$$, what is the magnitude $$|\vec{v}|$$?

Accepted Answer

$$5$$

Question 12

Convert the rectangular coordinates $$(0, -2) to $$polar coordinates.

Accepted Answer

$$(2, \dfrac{3\pi}{2})$$

Question 13

Which of the following is the correct Law of Cosines for a triangle with sides $$a$$, $$b$$, $$c$$ and angle $$C$$ opposite side $$c$$?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$\cos(C)$$

Question 14

Find the area of a sector with radius $$r = 6$$ and central angle $$	heta = 120$$^{\circ}$$.

Accepted Answer

$$12\pi$$

Question 15

Which of the following is the reference angle for $$210^{\circ}$$?

Accepted Answer

$$30^{\circ}$$

Question 16

If $$\sin$$^{-1}$$(x) = 	heta$$, what is the domain of $$\sin$$^{-1}$$(x)$$?

Accepted Answer

$$[-1, 1]$$

Question 17

Express $$\sin(x)\cos(y) as a $$sum using product-to-sum formulas.

Accepted Answer

$$\dfrac{1}{2}[\sin(x+y) + \sin(x-y)]$$

Question 18

A sound wave can be modeled by $$y = 0.5\sin(440\pi t). $$What is the period of this wave?

Accepted Answer

$$\dfrac{1}{220}$$

Question 19

Given $$\sec$$^{-1}$$(2)$$, what is its exact value in radians?

Accepted Answer

$$\dfrac{\pi}{3}$$

MAC 1114C College Trigonometry Syllabus and Course Overview

스터디 가이드 - 연습 문제

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