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NAME: Exam 4, Math 100, PreCalculus, Fall 2016, DeBonis (50 points) [1.] (12 points) Answer the following trigonometric questions: a. Convert π 9 to degrees. b. Compute sec 7π . 6 c. Given csc θ < 0 and sec θ = 3, find the value of tan θ. [2.] (9 points) Find all solutions to the following equation for 0 ≤ x < 2π (answers should be exact and in radians): 2 sin2 x + √ 3 sin x = 0 [3.] (10 points) Graph one cycle of the following trigonometric function: π f (x) = −2 cos 2πx + +1 2 [4.] (6 points) Verify the following trigonometric identity: (sin x + cos x)(tan x + cot x) = sec x + csc x [5.] (5 points) Rewrite the following without trigonometric functions: tan sec−1 √ x [6.] (8 points) Two poles of height 100 feet and 80 feet are attached by a wire (see diagram below) a. Find the exact value of d if θ = 60◦ . b. Find the value of θ to the nearest degree if d = 40 feet. [7.] (8 points) (Extra Credit) Estimate to the nearest degree the value of θ in the diagram below: