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Mathematics 120 test four Thursday, March 18, 2004 (1) Convert 120◦ to radians. (2) A central angle A intercepts an arclength s = 7 from a circle of radius r = 5. (see picture) Find the radian and degree measure of the angle A. (3) An central angle θ inside a unit circle is sketched below. Use the data to find exact values for cos θ = sin θ = tan θ = sec θ = csc θ = cot θ = (4) If cos B = − 25 and B is in quadrant three, find exact values (involving square roots when necessary) for sin B = (5) Show that tan θ + sec θ sin θ + 1 = 1 + sec θ cos θ + 1 tan B = page two (6) If θ = sin−1 m, then sin = and θ is between and . (7) Find the exact values (involving square roots when necessary): cos π 6 = tan (60◦ + k · 180◦ ) = (8) Use an angle subtraction formula to expand & simplify the quantity 8 cos θ − (Your answer will have the format a cos θ + b sin θ) (9) If x = 3 tan θ and θ is in quadrant 4, simplify the quantity √ 9 + x2 π 3 page three (10) Simplify each expression below: (a) sin sin−1 m = (b) cos sin−1 m = (11) Decide whether each of the following statements is true or false: • for any angle θ, sin 2θ = 2 sin θ. • for any second quadrant angle A and associated reference angle Ar , sin A = sin Ar . • for any angle θ in the domain of sec, sec(θ + π) = sec θ. • for any angle θ in the domain of csc, csc(−θ) = − csc θ. • Of the six graphs of the trig functions sin, cos, tan, csc, sec, and cot, exactly four of the graphs have vertical asymptotes. (12) Sketch a graph of the function y = 5 cos 8x − The graph should show all quarter-cycle points. π . 3 page four (13) Find all solutions θ, 0 ≤ θ < 360◦ for each trigonometric equation below: (round to the nearest degree) (a) tan θ = − 47 (b) sin 2θ = 5 6 (14) Given the sinusoidal graph below, find the function’s period = amplitude = frequency = horizontal shift = angular frequency = function’s equation: y = A sin(Bx + C) (what are A, B, & C) ?