Exam 4: Trigonometric Functions of Angles

If sinθ = , and the terminal side of θ lies in quadrant II, find secθ.

State in which quadrant or on what axis the terminal side of a 1373° angle in standard position lies.

Sprinkler: A sprinkler is set to reach an arc of 57 feet, 17 feet from the sprinkler. Through how many radians does the sprinkler rotate? Give the answer as a fraction.

The terminal side of an angle θ in standard position passes through the point (2, 5). Calculate the value of tanθ. Round your answer to four decimal places.

Use a calculator to approximate the sin 15.8° to three decimal places.

Use the reciprocal identity To calculate cot 60°.

If tan $\theta$ = , and the terminal side of $\theta$ lies in quadrant III, find csc $\theta$ .

Glide slope of an airplane. The glide slope of an airplane is the angle between the flight path approaching the runway and the ground. An airliner approaches a runway on a glide slope of approximately 3°. How long is the flight path of an approaching airliner if its height above the ground is 1,327 feet? Round your answer to the nearest whole foot.

State in which quadrant or on what axis the terminal side of a 1170° angle in standard position lies.

If tan $\theta$ = , and the terminal side of $\theta$ lies in quadrant II, find sin $\theta$ .

Low Earth Orbit Satellites. A low earth orbit (LEO) satellite is traveling in an approximately circular orbit 250 km above the surface of the Earth. If a ground station tracks the satellite when it is within a 69° cone above the tracking antenna (directly overhead), how many kilometers does the satellite travel during the ground station track? Assume the Earth has a radius of 6,400 km. Round to the nearest kilometer.

Use the triangle to write tan $\theta$ , if A = 5, B = 12, and C = 13.

Use the triangle with C = to find the exact cotθ. Rationalize the denominator and reduce the fraction if necessary.

Electric Motor. A 10-inch diameter pulley is being driven by an electric motor that is running at 600 revolutions per minute. If it is connected by a belt to a 15-inch diameter pulley that is driving a drill bit, what is the speed of the drill bit in revolutions per minute (rpm)? Round your answer to the nearest whole number.

Find the area of the circular sector with a radius r = 8.6 in and central angle θ = °. Round your answer to one decimal place.

A car owner decides to upgrade from tires with a diameter of 24.5 inches to tires with a diameter 26.6 inches. If she doesn't update the onboard computer, how fast will she be traveling when the speedometer reads 67 mph? Round to the nearest mph.

State in which quadrant or on which axes the angles with the given measure in standard position would lie.

Big Ben. The Big Ben clock tower in London has clocks on all four sides. If each clock has a minute hand that is 11.5 feet in length, how far does the tip of each hand travel in 55 minutes? Round to the nearest integer.

Calculate cscθ if θ is in standard position and has a measure of 1890°.

Electronic Signals. Two electronic signals that cancel each other out are said to be 180° out of phase, or the difference in their phases is 180°. How many radians out of phase are two signals whose phase difference is 66°?