HW3sol - MAC1114 Homework 3 Due Thursday January 27 1...

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Unformatted text preview: MAC1114 - Homework 3 Due Thursday, January 27 1. Memorize the rst quadrant of the unit circle. Don't turn anything in for this, but do it. 2. Suppose cot θ = − 24 . Find the remaining ve trig functions (show your work!) if: 7 (a) θ lies in Quadrant II. In Quadrant II, cos θ < 0 and sin θ > 0. Since cot θ gives us information about the opposite and adjacent sides, to nd the hypotenuse, we use the Pythagorean theorem: 72 + 242 = c2 ⇒ c = 25. 7 24 7 The other ve trig functions are then: sin θ = 25 , cos θ = − 25 , tan θ = − 24 , sec θ = − 25 , 24 csc θ = 25 7 (b) θ lies in Quadrant IV. 7 This is the same as part (a) except now cos θ > 0 and sin θ < 0. So we instead have sin θ = − 25 , 24 7 25 25 cos θ = 25 , tan θ = 24 , sec θ = 24 , csc θ = − 7 . 3. A land surveyor is trying to compute the height of a mountain in the distance. She knows that the base of the mountain is about ve miles away. Using a clinometer, she observes an angle of elevation of 6.48◦ . How high is the mountain, in feet? Here is the picture I sent in an e-mail as a hint: To solve for h, all you need to do is set tan 6.48◦ = h , then get h = 5 tan 6.48◦ . To convert to 5 feet, multiply by 5280, so you get h = 26400 tan 6.48◦ . You do not need to compute tan 6.48◦ in the calculator, but it's ne if you did. 1 ...
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