A ferris wheel with a radius of 25 meters makes one rotation every 36 seconds. At the bottom of the ride, the passenger is 1 meter above the ground.

a) Let h be the height, above ground, of a passenger. Determine h as a function of time if h = 51 meter at t = 0.

b) Find the height h after 45 seconds.

Linda measures the angle of elevation from a point on the ground to the top of the tree and find it to be 35^{o}. She then walks 20 meters towards the tree and finds the angle of elevation from this new point to the top of the tree to be 45^{o}. Find the height of the tree. (Round answer to three significant digits)

From the top of a cliff 200 meters high, the angles of depression of two fishing boats in the same line of sight on the water are 13 degrees and 15 degrees. How far apart are the boats? (Round your answer to 4 significant digits)

The graph of function f is the graph of function g(x) = a sin(x - pi/3) translated vertically by 2. Also f(pi/2) = 1. Find a formula in terms of x for function f.

Find sin(x) and tan(x) if cos(pi/2 - x) = - 3/5 and sin(x + pi/2) = 4/5?

Find the exact value of [ tan (25^{o})+ tan (50^{o} ] / [ 1 - tan( 25^{o}) tan(50^{o}) ]

What is the angle B of triangle ABC, given that A = 46^{o}, b = 4 and c = 8?(Note: side a faces angle A, side b faces angle B and side c faces angle C).

Find the exact value of tan (s + t) given that sin s = 1/4, with s in quadrant 2, and sin t = -1/2, with t in quadrant 4.

Find all angles of a triangle with sides 9, 12 and 15.

Write an equation for a sine function with an amplitude of 5/3 , a period of pi/2, and a vertical shift of 4 units up.

Find the exact values of cos (13pi/12).

Two gears are interconnected. The smaller gear has a radius of 4 inches, and the larger gear has a radius of 10 inches. The smaller gear rotates 890 degrees in 4 seconds. What is the angular speed, in degrees per minute, of the larger rotate?

A ladder of length 20 meters is resting against the wall. The base of the ladder is x meters away from the base of the wall and the angle made by the wall and the ladder is t.

a) Find x in terms of t.

b) Starting from t = 0 (the ladder against the wall) and then gradually increase angle t; for what size of angle t will x be the quarter of the length of the ladder?