Exam 3: Radian Measure

Two cities are approximately 550 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side. a = 550 __________ radians

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. ​ __________

An arc of length 2 feet is cut off by a central angle of  radians. Find the area of the sector formed. ​

Convert to degree measure. ​

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 = 335°, r = 5 inches. If the answer needs rounding, round it to three significant digits. s = __________ inches

Find the exact value of  . ​

The pendulum on a grandfather clock swings from side to side once every second. If the length of the pendulum is 5 feet and the angle through which it swings is 22°, how far does the tip of the pendulum travel in 1 second? ​

A lawn sprinkler is located at the corner of a yard. The sprinkler is set to rotate through 90 and project water out 50 feet. What is the area (rounded to three significant digits)of the yard watered by the sprinkler? ​

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

Find the angular velocity associated with the given rpm. ​ If the answer needs rounding, round it to three significant digits. __________ rad/min

Graph the unit circle using parametric equations with your calculator set to radian mode. Use a scale of . Trace the circle to find all values of t between 0 and 2 π satisfying the following statement. Round your answers to the nearest ten-thousandth. ​

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. ​

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

An arc of length 3 feet is cut off by a central angle of  radians. Find the area of the sector formed. If the answer needs rounding, round it to three significant digits. A = __________ ft²

Point P moves with angular velocity ω  on a circle of radius r . Find the distance s traveled by the point in time t . Round to a whole number. ​

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/sec

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

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

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 = 30°, r = 2  mm. If the answer needs rounding, round it to three significant digits. s = __________ mm

Use the unit circle to find the six trigonometric functions of . ​