a) Determine the exact radian measure of 100^o

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

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?

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

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.

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.

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

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

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

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.

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

\displaystyle \sec x - 5 =0

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

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

As a science project, Anwar monitored the content of carbon monoxide outside his house in the city over several days. He found that it reached a maximum of about 30 ppm (parts per million) at 6:00 P.M., and a minimum of 10 ppm at 6:00 A.M.

a) Select a point on the graph where the instantaneous rate of change of the carbon monoxide level appears to be a maximum.

b) Use a method similar to that in Example 1 of Section 5.5 to estimate the instantaneous rate of change of the carbon monoxide level at this point, to one decimal place.