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

\displaystyle \frac{\pi}{8} 

Q1a

\displaystyle 4\pi 

Q1b

\displaystyle 5 

Q1c

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

Q1d

\displaystyle 125^o 

Q2a

\displaystyle 450^o 

Q2b

\displaystyle 5^o 

Q2c

\displaystyle 330^o 

Q2d

\displaystyle 215^o 

Q2e

\displaystyle 5^o 

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.

Q3

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

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

Q4a

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

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

Q4b

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

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

Q4c

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

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

Q4d

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

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

Q4e

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

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

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)

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)

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)

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)

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)

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)

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}) 

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}) 

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}) 

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}) 

Q6d

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

\displaystyle y = \sin x 

Q7a

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

\displaystyle y = \cos x 

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 

Q7c

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

y = \tan x

Q8a

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

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

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 

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}) 

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 

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