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Math 142 Hand-in Homework #4 Name: 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