MTH 112 - Winter 2019 - Written Homework 1
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(1) What is the arc length swept out by an angle of 160◦ on a circle of radius 3?
(2) Convert 80◦ to radians.
(3) Convert
6π
radians to degrees.
5
(4) Find the area of the workspace of a robotic arm that can rotate between 10◦ and
130◦ . The length of the robotic arm can vary between 5 inches and 20 inches. Give
your answer to the nearest tenth and include units.
MTH 112 - Winter 2019 - Written Homework 1
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(5) The planet Mars has a radius of 2,000 miles and rotates one revolution every 24 hours.
Find the angular velocity and the linear speed of a point on its equator.
(6) Two cities have nearly the same longitude of 115◦ W. The latitude of the first city is
25◦ 200 and the latitude of the second city is 33◦ 340 . Approximate the distance between
the cities if the average radius of the Earth is 3955 miles.
MTH 112 - Winter 2019 - Written Homework 1
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(7) One of the most common ways to measure wind speed is with an anemometer, as
shown in the figure below. The cups catch the wind and cause the vertical shaft to
rotate. At lower wind speeds, the cups move at approximately the same speed at the
wind. If that cups are rotating 5 times per second with a radius of 6 inches, compute
the wind speed in miles per hour.
MTH 112 - Winter 2019 - Written Homework 1
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(8) The angle of elevation from a point on the ground to the top of a pyramid is 22◦ 400 .
The angle of elevation from a point 171 feet farther back to the top of the pyramid is
15◦ 300 . Find the height of the pyramid.
(9) The figure shows a satellite in orbit above the Earth. If θ = 66.5◦ , find the altitude
of its orbit. The equatorial radius of Earth is 3963 miles.