Mid Chapter Review on Trig Functions
Chapter
Chapter 6
Section
Mid Chapter Review on Trig Functions
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Solutions 37 Videos

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

\displaystyle \frac{\pi}{8}

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Q1a

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

\displaystyle 4\pi

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Q1b

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

\displaystyle 5

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Q1c

Convert each angle from radians to degrees. Express your answer to one decimal place, if necessary.

\displaystyle \frac{11\pi}{12}

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Q1d

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

\displaystyle 125^o

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Q2a

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

\displaystyle 450^o

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Q2b

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

\displaystyle 5^o

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Q2c

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

\displaystyle 330^o

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Q2d

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

\displaystyle 215^o

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Q2e

Convert each angle from degrees to radians. Express your answer to one decimal place, if necessary.

\displaystyle 5^o

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Q2f

A tire with a diameter of 38 cm rotates 10 times in 5 s.

a) What is the angle that the tire rotates through, in radians, from 0 s to 5 s?

b) Determine the angular velocity of the tire.

c) Determine the distance travelled by a pebble that is trapped in the tread of the tire.

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Q3

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

\displaystyle \sin \frac{3\pi}{4}

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Q4a

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

\displaystyle \sin \frac{11\pi}{6}

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Q4b

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

\displaystyle \tan \frac{5\pi}{3}

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Q4c

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

\displaystyle \tan \frac{5\pi}{6}

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Q4d

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

\displaystyle \cos \frac{3\pi}{2}

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Q4e

Sketch each angle in standard position, and then determine the exact value of the trigonometric ratio.

\displaystyle \cos \frac{4\pi}{3}

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Q4f

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

(-3, 14)

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Q5a

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

(6, 7)

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Q5b

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

(1, 9)

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Q5c

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

(-5, -18)

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Q5d

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

(2, 3)

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Q5e

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

(4, -20)

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Q5f

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

\displaystyle \sin (- \frac{7\pi}{6})

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Q6a

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

\displaystyle \cot ( \frac{7\pi}{4})

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Q6b

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

\displaystyle \sec ( -\frac{\pi}{2})

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Q6c

The terminal arms of angles in standard position pass through the following points. Find the measure of each angle in radians, to the nearest hundredth.

\displaystyle \cos ( -\frac{5\pi}{6})

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Q6d

State the x-intercepts and y-intercepts of the graph of the following functions.

\displaystyle y = \sin x

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Q7a

State the x-intercepts and y-intercepts of the graph of the following functions.

\displaystyle y = \cos x

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Q7b

State the x-intercepts and y-intercepts of the graph of the following functions.

State the x-intercepts and y-intercepts of the graph of the following functions.

\displaystyle y = \tan x

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Q7c

Sketch the graph of each function on the interval \displaystyle -2\pi \leq x \leq 2\pi .

y = \tan x

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Q8a

Sketch the graph of each function on the interval \displaystyle -2\pi \leq x \leq 2\pi .

\displaystyle y = 2\sin(-x) - 1

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Q8b

Sketch the graph of each function on the interval \displaystyle -2\pi \leq x \leq 2\pi .

\displaystyle y =\frac{5}{2} \cos(2(x + \frac{\pi}{4})) + 3

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Q8c

Sketch the graph of each function on the interval \displaystyle -2\pi \leq x \leq 2\pi .

\displaystyle y = - \frac{1}{2} \cos(\frac{1}{2}x - \frac{\pi}{6})

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Q8d

Sketch the graph of each function on the interval \displaystyle -2\pi \leq x \leq 2\pi .

\displaystyle y = 2\sin(-(x - \frac{\pi}{2}))+ 4

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Q8e

Sketch the graph of each function on the interval \displaystyle -2\pi \leq x \leq 2\pi .

\displaystyle y = 0.4 \sin(\pi - 2x) - 2.5

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Q8f