Exam 3: Radian Measure

If angle θ  is in standard position and intersects the unit circle at  find  and . ​

The current San Francisco cable railway is driven by two large 12-foot-diameter drive wheels, called sheaves. Because of the figure-eight system used, the cable subtends a central angle of 270° on each sheave. Find the length of cable riding on one of the drive sheaves at any given time. ​ a = 12 ft If the answer needs rounding round it to three significant digits. __________ feet

For the following expression, find the value of y that corresponds to each value of x , then write your results as ordered pairs ( x, y ).  for 

Use a calculator to find tan 143.8°. Please round the answer to the nearest ten-thousandth.

Find the exact value of .

Find the linear velocity of a point moving with uniform circular motion, if the point covers a distance s in an amount of time t , where ​ mi and hr ​

Convert to radian measure using exact values. θ = 340° ​

Find the radian measure of angle θ , if θ  is a central angle in a circle of radius r , and θ  cuts off an arc of length s . r = 5 inches, s = 25 inches θ =  __________ radians

Find the exact value of .

Use a calculator to find Please round the answer to the nearest thousandth.

Label the reference angle in both degrees and radians. ​

θ  is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 9°,   m . ​

Find the distance s covered by a point moving with linear velocity v for a time t if ​ ft/sec and sec ​

Use the unit circle to find all values of θ  between 0 and 2 π  for which .

θ  is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 3°,  m . If the answer needs rounding, round it to three significant digits. r = __________ m

A woman rides a bicycle for 2 hours and travels 32 kilometers (about 20 miles). Find the angular velocity of the wheel if the radius is 30 centimeters. ​

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find the sine and cosine of  to the nearest ten-thousandth. __________ ​ __________

Name the reference angle in both degrees and radians. θ = 170° ​

The San Francisco cable cars travel by clamping onto a steel cable that circulates in a channel beneath the streets. This cable is driven by a large 14-foot-diameter pulley, called a sheave (see the figure). The sheave turns at a rate of 17 revolutions per minute. Find the speed of the cable car, in miles per hour (rounded to three significant digits), by determining the linear velocity of the cable. (1 mi = 5,280 ft). ​

Use a calculator to convert 100°10' to radians. Round your answer to the nearest hundredth. (First convert to decimal degrees, then multiply by the appropriate conversion factor to convert to radians.) ​