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# quiz11solutions - MAC1147 Quiz#11 In the top-right corner...

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Unformatted text preview: MAC1147: Quiz #11 12/1/2009 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. An airplane 5 miles in the air measures the angles of depression to two cars on a straight highway to be 30◦ and 45◦ . What is the distance between the two cars, in miles? After drawing an appropriate picture, the following equations are suggested by the two right triangles: tan 30◦ tan 45◦ = = 5 x+ y 5 x , where x represents the distance from the rst car to the plane, and y represents the distance between the rst and second cars. The second equation quickly gives x = 5, so plugging this into the rst equation gives: √ √ √ 5 3 = ⇒ y + 5 = 5 3 ⇒ y = 5( 3 − 1) miles. 3 5+y sin x in nonfractional form. 1 − cos x sin x(1 + cos x) sin x(1 + cos x) cos x sin x 1 + cos x 1 · = = + = csc x+cot x = 2 1 − cos x 1 + cos x 1 − cos2 x sin x sin x sin x 2. Rewrite 1 = sin x cos x tan x + cot x 1 1 1 1 = = = = sin x cos x 2 2 1 sin x cos x tan x + cot x sin x + cos x + sin x cos x cos x sin x sin x cos x 3. Verify the trigonometric identity: 1 ...
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