Exam 3: Radian Measure

The pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 4 feet and the angle through which it swings is 23°, how far does the tip of the pendulum travel in 1 second? If the answer needs rounding, round it to three significant digits. __________ feet

Find the exact value of  . ​

The figure is a model of George Ferris's Ferris wheel. The diameter of the wheel is 245 feet; and θ  is the central angle formed as a rider travels from his or her initial position P ₀ to position P ₁. Find the distance traveled by the rider if θ = 216° . ​

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

The earth rotates through one complete revolution every 1,440 minutes. Since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 1,440 minutes. Find the angular velocity of a person standing on the equator. If the answer needs rounding, round it to five decimal places. __________ rad/min

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 ​ cm and sec If the answer needs rounding, round it to three significant digits. __________ cm/sec

For the problem below, θ  is a central angle in a circle of radius r . Find the length of arc s cut off by θ . θ = 25°, r = 3  mm. ​

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

Point P moves with angular velocity ω  on a circle of radius r . Find the distance s traveled by the point in time t . ​ If the answer needs rounding, round it to the whole number. __________ m

Find the angular velocity associated with the given rpm. 9.6 rpm If the answer needs rounding, round it to the nearest tenth. __________ rad/min

A Ferris Wheel called Colossus has a diameter of 164 feet. Using the figure as a model, find the distance traveled by someone starting at initial position P ₀ and moving to position P ₁ if θ = 157°. ​

Give the exact value of .

Point P sweeps out central angle θ  as it rotates on a circle of radius r . Find the angular velocity of point P . ​ If the answer needs rounding, round it to three significant digits. __________ rad/min

Find the exact value of cos 135º. ​

Through how many radians does the minute hand of a clock turn during a 5-minute period? ​

Point P sweeps out central angle θ  as it rotates on a circle of radius r . Find the angular velocity of point P . ​ If the answer needs rounding, round it to the whole number. __________ rad/hr

Find the distance s covered by a point moving with linear velocity v for a time t if ​ ​ If the answer needs rounding, round it to three significant digits. __________ mi

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 Please round the answer to the nearest ten-thousandth. ​

Use a calculator to find θ  to the nearest tenth of a degree, if and ​ with θ  in QII ​ __________°