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c2 = a2 + b2 − 2ab cos C name: s A 1 + cos A cos = ± 2 2 Mathematics 142 second test Wednesday, May 13, 2009 please show your work to get full credit s A 1 − cos A sin = ± 2 2 1–2. Find the exact value of each expression by using an angle addition or subtraction formula. 1. sin 65◦ cos 70◦ + cos 65◦ sin 70◦ 2. cos 230◦ cos 80◦ + sin 230◦ sin 80◦ 3–4. Find all the solutions between 0 and 2π for each trigonometric equation: √ 3. cot θ + 3 (csc θ − 2) = 0 4. cos 2θ + 4 sin2 θ = 0 page two √ 5. Convert (x, y) = (4, −4 3) to polar coordinates (r, θ). 6. Convert the polar equation r = 4 cos θ to an equation involving x and y. (HINT: First multiply both sides of the equation by r.) 7–8. Solve for the indicated side length or angle measure: 4 90° 20 x A 5 25° 10 A page three 9. Show that 5 cos2 θ + 2 sin2 θ = 5 − 3 sin2 θ. 10. Use the data sin A = 2 and A is in quadrant two 3 cos B = 1 and A is in quadrant one 4 to compute exact values of (a) cos A and sin B (b) cos(A + B) (c) sin 2A (d) cos B 2 page four 11. Use the graph of polar coordinate r versus direction angle θ ( in degrees ) to draw the corresponding polar graph: 3 r 2 1 0 ‐210 ‐180 ‐150 ‐120 ‐90 ‐60 ‐30 ‐1 ‐2 ‐3 waterproof – paper.com 0 30 60 θ 90 120 150 180 210 page four 12. Show that cos tan−1 v = √ 1 1 + v2 13. Show that cos(5θ − θ) − cos(5θ + θ) = 2 sin 5θ sin θ