Cumulative Review of Trig Ch4 and 5
Chapter
Chapter 5
Section
Cumulative Review of Trig Ch4 and 5
Solutions 22 Videos

a) Determine the exact radian measure of 100^o

b) Determine the exact degree measure of \frac{7\pi}{12}

Q1

A gymnasium has a circular running track around the mezzanine with a radius of 20 m. A runner ran along the arc of the track for 60 m. What is the sector angle, in radians, from the start to the finish of his run?

Q2

Determine an exact value for \sin \frac{3\pi}{4} - \tan \frac{5\pi}{4}

Q3

Two guy wires are attached to the top of a radio antenna 25 m in height. The wires make angles of \displaystyle \frac{\pi}{6}  and \displaystyle \frac{\pi}{4}  with the ground, as shown.

Determine an exact expression for the distance between the two anchor points of the wires, A and B.

Q4

Given that \cos \frac{7\pi}{15} \doteq 0.1045, use an equivalent expression to determine \sin \frac{29\pi}{30}, to four decimal places.

Q5

If \sin y = \cos 3y, determine an exact valeu for \angle y.

Q6

Prove \displaystyle \frac{\sin 2x}{\sec x} = \frac{2\cos^2x}{\csc x} 

Q10

Prove \displaystyle \sin(x + y)\cos(x -y) = \frac{\sin x}{\sec x} + \frac{\cos y}{\csc y} 

Q11

Commercial bottling machines often use a circular drum as part of a mechanism to install tops on bottles.

One such machine has a diameter of 120 cm, and makes a complete turn once every 5 s.

A sensor at the left side of the drum monitors its movement. Take the sensor position as zero.

a) Model the horizontal position of a point on the drum, h, in centimetres, as a function of time, t, in seconds.

b) Sketch a graph of h versus t over two cycles.

c) If the technician monitoring the machine increases the speed to complete a cycle in 3 5, what changes would occur in your model? Justify your answer.

Q17

Find x \in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle \sec x - 5 =0 

Q18a

Find x \in [0, 2\pi] to the nearest hundredth of a radian.

\displaystyle 12 \sin^2x - \sin x - 1= 0