Trigonometry Answers

Show the derivation of the formula.

Cos u/2=±√1+cos u/2.

Show the derivation of the formula.

Sin (u-v)=sin u cos v -cos u sin v

Show the derivation of the formula.

Cos (u+v)=cos u cos v - sin u sin v

find the remaining parts of the quadrantal spherical triangles (c=90°) given the following, giveb parts b= 45°20 a=76°40

A passenger in an airplane at an altitude of 10 kilometers sees two towns directly to the east of the plane. The angles of depression to the towns are 𝛽 = 21° and 𝜃 = 59° (see figure). How far apart are the towns? (Round your answer to one decimal place.)

 km

A conveyor is used to lift paper to a shredder. The most efficient operating angle of elevation for the conveyor is 37.8°. The paper is to be elevated 16.0 m. What length (in m) of conveyor is needed? (Round your answer to three significant digits.)

A bullet is found embedded in the wall of a room 3.2 m above the floor. The bullet entered the wall going upward at an angle of 34.3°. How far from the wall was the bullet fired if the gun was held 1.5 m above the floor?

Fire tower A is x = 29 kilometers due west of tower B. A fire is spotted from the towers, and the bearings from A and B are 𝜃 = N 78° E and φ = N 54° W, respectively (see figure). Find the distance d of the fire from the line segment AB. (Round your answer to two decimal places.)

A cadet rappelling down a cliff on a rope needs help. A cadet on the ground pulls tight on the end of the rope that hangs down from the rappelling cadet to lock the cadet in place. The length of the rope between the two cadets is 129 feet, and the angle of elevation of the rope is 75°. How high above the ground is the cadet on the rope? (Round your answer to two decimal places.)

The diameter of a Ferris wheel is 10 meters. From a platform 2 meters above the ground, you board the Ferris wheel at the bottom. Determine an equation for a rider's height in relation to time if it takes 35 seconds to reach the summit. Sketch the graph.