Exam 3: Radian Measure

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

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 12-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, by determining the linear velocity of the cable. (1 mi = 5,280 ft)​ ​ If the answer needs rounding, round it to the nearest hundredth. __________ mph

If we start at the point (1, 0)and travel once around the unit circle, we travel a distance of 2 π  units and arrive back where we started at the point (1, 0). If we continue around the unit circle a second time, we will repeat all the values of x and y that occurred during our first trip around. Use this discussion to evaluate the expression. ​

Use a calculator to convert 150°50' 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.)__________ radians

A sector of area  in² is formed by a central angle of 45 . What is the radius of the circle? ​

If we start at the point (1, 0)and travel once around the unit circle, we travel a distance of 2 π  units and arrive back where we started at the point (1, 0). If we continue around the unit circle a second time, we will repeat all the values of x and y that occurred during our first trip around. Use this discussion to evaluate the expression.

Find the area of the sector formed by central angle θ = 2.6 in a circle of radius r = 4 inches. If the answer needs rounding, round it to three significant digits. A = __________ in²

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

θ  is a central angle that cuts off an arc of length s . Find the radius of the circle if θ = 153°, s = 5 km . ​

Give the exact value of .

Evaluate the expression when x is . Use exact values. 7 cos 3 x ​

The figure below is a model of the Ferris wheel. The diameter of the wheel is 193 feet, and one complete revolution takes 17 minutes. Find the linear velocity of a person riding on the wheel. Give your answer in miles per hour and round to the nearest hundredth. ​

If the distance to the sun is approximately 93 million miles, and, from the earth, the sun subtends an angle of approximately 0.5°, estimate the diameter of the sun to the nearest 10,000 miles. __________ miles

Find the exact value of Express your answer in simplified form. Do not convert to decimal form.

Give the exact value of . ​

Graph the unit circle using parametric equations with your calculator set to degree mode. Use a scale of 5. Trace the circle to find all values of t between 0° and 360° satisfying the statement. ​

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 = 4 inches, s = 20 inches ​

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 If the answer needs rounding, round it to three significant digits. __________ mph

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

A light truck with manual transmission has a circular brake drum with a diameter of 317 millimeters. Each brake pad, which presses against the drum, is 308 millimeters long. What central angle is subtended by one of the brake pads? Write your answer in both radians and in degrees. ​a = 308  millimeters, b = 317  millimeters ​