Math 142 Hand-in Homework #4

Math 142 Hand-in Homework #4
Due Tuesday July 19th
Show all work. Correct answers without justification may not get credit.
1. Suppose that a movie theater has a screen that is 28 feet tall. When you sit down, the
bottom of the screen is 6 feet above your eye level. The angle formed by drawing a line
from your eye to the bottom of the screen and your eye and the top of the screen is
called the viewing angle. In the figure below θ is the viewing angle.
What is the viewing angle if you sit 10 ft from the screen?
What about 15 ft?
Find an expression for θ if you sit x ft from the screen.
2. Establish each of the following identities:
(a) (sin x − cos x)2 = 1 − 2 sin x cos x
(b) (1 − cos2 θ)(1 + cot2 θ) = 1