University:
Santa Ana College
Course:
MATH 170 | Pre-Calculus Mathematics
Academic year:

2023
Views:

53

Pages:

6
Author:

cmjnlandxc19

Math 170 Exam: Trigonometry Solve each by the methods demonstrated in class, give exact answers where possible, put a box around your final answer. 1) Find the exact value of each: a) sin(2π/3) = √3/2 b) cos(7π/4) = √2/2 c) csc(-11π/4) = -√2 d) tan(7π/4) = -1 e) cot(-7π/2) = 0 2) Find the exact value of each: a) If cos x = -4/7 and x is in Quadrant III, find sin2x. sin2x = 2sin(x)cos(x) = 2(-√33/7)(-4/7) = 8√33/49 b) sin²(π/5) + cos²(π/5) = 1 c) Given sec θ = -2 and tan θ > 0, find each: cos θ = -1/2 sin θ = √3/2 tan θ = √3 3) Sketch 2 periods of each: state the amplitude, period, and any phase shift of each graph. Label all key points. a) y = 3sin(2x) Amplitude: 3 Period: 2π / 2 = π Phase shift: 0 b) y = -cos(x - π/3) Amplitude: 1 Period: 2π Phase shift: π/3 4) Simplify each to a single trig function: a) (sec x - cos x) / tan x = sin x b) (sin x csc x) / tan x = cot x c) (1 + sec x) / (sin x + tan x) = csc x 5) Solve each. Include a picture with each. a) From the top of a 250-foot lighthouse, the angle of depression to a ship in the ocean is 18 degrees. Approximately how far is the ship from the base of the lighthouse? [Diagram: A lighthouse with a height of 250 feet. An angle of depression of 18 degrees is formed between the top of the lighthouse and a ship in the ocean.] tan(18) = 250 / x x = 250 / tan(18) x ≈ 769.4 ft The ship is about 769.4 ft away. b) A radio transmission tower sits atop a building. At a point 550 feet from the base of the building, the angle of elevation to the bottom of the radio transmission tower and to a point on the top of the tower is 31 degrees and 43 degrees respectively. Find the height of the radio tower to the nearest foot. [Diagram: A building with a radio tower on top. Angles of elevation of 31 degrees and 43 degrees are formed from a point 550 feet away from the base of the building.] tan(31) = H / 550 H = 550 * tan(31) ≈ 330.49 ft tan(43) = (H + T) / 550 T = 550 * tan(43) - H ≈ 182 ft The tower is about 182 ft.

Math 170 Exam Trigonometry Solutions

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