Exam 3: Radian Measure and the Unit Circle

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$

Find the exact circular function value. - $\cot \frac { - 11 \pi } { 6 }$

Solve the problem. -Let angle POQ be designated ϴ. Angles PQR and VRQ are right angles. If ϴ = 45°, find the exact length of VR.

Solve the problem. -Suppose the tip of the minute hand of a clock is 5 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 5.5 hours. Give an exact answer.

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \tan ^ { 2 } \mathrm {~s} = \frac { 1 } { 3 }$

Find the exact value without using a calculator. - $\tan \frac { 5 \pi } { 4 }$

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

Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

Find the specified quantity. - $\text { Is it correct to say that the value of } \tan 30 = \frac { \sqrt { 3 } } { 3 } \text { ? Explain your answer. }$

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

Use a table or a calculator to evaluate the function. Round to four decimal places. -sin 0.2300

Use a table or a calculator to evaluate the function. Round to four decimal places. -tan 0.2491

Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 16.12 \mathrm { ft } ; \theta = \frac { \pi } { 11 }$ radians

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. $\text { Use } 3.1416 \text { for }$ -5

Solve the problem. -A pulley of radius 25 cm rotates 7 times in 4 sec. Find the angular speed of the pulley.

Solve the problem. -A car wheel has a 14-inch radius. Through what angle (to the nearest tenth of a degree)does the wheel turn when the car rolls forward 3 ft?

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

Solve the problem. -Find v for the tip of the hour hand of a clock, if the hand is 7 cm long.

Solve the problem. -Find $\omega$ for a spoke on a bike tire revolving 60 times per minute.

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