Exam 3: Radian Measure and the Unit Circle

Solve the problem. -A pendulum swings through an angle of $18 ^ { \circ }$ each second. If the pendulum is $20 \mathrm {~cm}$ in length and the complete swing from right to left lasts 2 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \cos \mathrm { s } = - \frac { \sqrt { 2 } } { 2 }$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

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

Solve the problem. -The maximum afternoon temperature in Granderson is modeled by $t = 62 - 30 \cos \frac { x \pi } { 6 }$ where $t$ represents the maximum afternoon temperature in degrees Fahrenheit in month $x$ , with $x = 0$ representing January, $x = 1$ representing February, and so on. Find the maximum afternoon temperature in June.

For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s. -s = 47

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. -v = 218.9 m per sec, Ɯ = 0.63361 radian per sec (Round to four decimal places when necessary.)

Use a table or a calculator to evaluate the function. Round to four decimal places. -csc 0.2475

Solve the problem. -A wheel is rotating at 4 radians per sec, and the wheel has a 96-inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?

Convert the degree measure to radians. Leave answer as a multiple of π. -1800°

Solve the problem. -Find the radius (to the nearest hundredth of a millimeter)of a pulley if rotating the pulley 109.38° raises the pulley 42.2 mm.

Use the formula s = rωt to find the value of the missing variable. Give an exact answer. - $\mathrm { s } = \frac { \pi } { 3 } \mathrm {~m} , \mathrm { r } = 3 \mathrm {~m} , \mathrm { t } = 4 \mathrm { sec }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin s = \frac { \sqrt { 3 } } { 2 }$

Solve the problem. -The angle of elevation $\theta$ of the sun in the sky at any latitude $L$ is calculated with the formula $\sin \theta = \cos \mathrm { D } \cos \mathrm { L } \cos \omega + \sin \mathrm { D } \sin \mathrm { L }$ . $\omega$ is the number of radians that the Earth has rotated through since noon when $\omega = 0$ . D is the declination of the sun. Westville has latitude $L = 36.5 ^ { \circ }$ . Find the angle of elevation $\theta$ in degrees of the sun at 3 PM on February 29, 2012, where at that time $\mathrm { D } \approx - 0.1425$ and $\omega \approx 0.7854$ .

Find the exact circular function value. - $\cot \pi$

Find the exact circular function value. - $\sin \frac { - 5 \pi } { 4 }$

Convert the degree measure to radians. Leave answer as a multiple of π. -510°

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City E, 35° N and City F, 44° S. (Round to the nearest kilometer.)

$\text { Find the value of s in the interval } [ 0 , \pi / 2 ] \text { that makes the statement true. Round to four decimal places. }$ -sec s = 3.7404

Solve the problem. -A bicycle with a 26-inch wheel (diameter)travels a distance of 200 feet. How many revolutions does the wheel make (to the nearest revolution)?