Exam 3: Radian Measure and the Unit Circle

Solve the problem. -Suppose the tip of the minute hand of a clock is 5 in. from the center of the clock. Determine the distance traveled by the tip of the minute hand in $3 \frac { 1 } { 2 }$ hours. Give an exact answer.

Find the exact value without using a calculator. - $\cot \pi$

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 13°, find the length of US accurate to four decimal places.

Find the exact value without using a calculator. - $\cot \left( \frac { - 5 \pi } { 6 } \right)$

Convert the degree measure to radians. Leave answer as a multiple of $\pi \text {. }$ - $36 ^ { \circ }$

Solve the problem. -The minute hand of a clock is 13 inches long. What distance does its tip move in 16 minutes? Give an exact answer.

For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s. -s = 66

Suppose an arc of length $s$ lies on the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ , starting at point $( 1,0 )$ and terminating at the point ( $x$ , $y$ ). Use a calculator to find the approximate coordinates $( x , y )$ . Round coordinates to four decimal places when appropriate. The unit circle $x ^ { 2 } + y ^ { 2 } = 1$ -s = 5.6

Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place. -r = 115.19 in.; ϴ = 195°

Find the exact value without using a calculator. - $\cos 2 \pi$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 3 \pi } { 8 }$

Find the exact circular function value. - $\cos 2 \pi$

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ --470°

The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of . - $\text { Find } \cos \theta \text {. }$

Solve the problem. -A wheel is rotating at 5 radians/sec, and the wheel has a 83-inch diameter. To the nearest foot, what is the speed of a point on the rim in ft/min?

Find the exact value without using a calculator. - $\sin \frac { 3 \pi } { 4 }$

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ --45°

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- 13 \pi$

Solve the problem. -A circular sector has an area of 18 in $^ { 2 }$ and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.

Solve the problem. -The temperature in Verlander is modeled by $\mathrm { T } ( \mathrm { x } ) = 41 \sin \left[ \frac { 2 \pi } { 365 } ( \mathrm { x } - 102 ) \right] + 44$ where $\mathrm { T } ( \mathrm { x } )$ is the temperature in degrees Fahrenheit on day $x$ , with $x = 1$ representing January 1 and $x = 365$ representing December 31 . Find the temperature on July 7 .