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PreCalculus Semester 2 Review Use a separate sheet of paper to do your work. 1. a) Convert to degrees: 7 12 b) Convert to radians: 27° 4.1 2. A man that is 6 feet tall casts a shadow 10 feet long. Find the angle of elevation of the sun 4.3 3. Use trigonometric identities to simplify the expression: 4.3/5.1 a) 1 cos 1 cos c) b) cot 2 x sin 2 x sin 2 cos 2 d) sec 2 x 1 cot 2 x 3 4. Given sin and tan 0 , find cot 5 4.4 5. Graph each equation. 4.5 1 (a) y cos x 2 (b) y sin4 x 1 (c) y cos 2 x 4 (d) y 3 sin 6. Evaluate: 3 a) arcsin 2 x 4 4.7 2 b) arccos 2 c) arctan 1 2 7. Evaluate: sin arccos 3 8. Simplify: a) sec x sin 2 x cos x 9. Simplify: sin x cot x cos x 4.7 b) 1 1 sin 2 x 5.1 5.1 10. Evaluate: a) sin 5.4 11 11 3 , Use the fact that 12 12 4 6 b) cos 105, Use the fact that 105 60 45 11. Simplify: cos 2 5.4 12. Find all the solutions in the interval 0,2 : 2 sin x 2 0 5.3 13. Find all the solutions in the interval 0,2 : cot x cos 2 x 2 cot x 5.3 14. Find all the solutions in the interval 0,2 : sin 2 x cos x 0 5.3/5.5 15. Find all the solutions in the interval 0,2 : tan 2 x 3 0 5.3 16. Find the area of the triangle. 6.2 6 8 12 17. Find the value of x. 6.1 10 12 46º x 18. a = 10, b = 4.5, C = 105° Find side c. 6.2 19. B = 150°, a = 10, c = 20 Find angle A. 6.2 20. B = 110°, a = 125, b = 100 Find side c. 6.1 21. Find the value of x for the following 45° - 45° - 90° triangles. x 6 2 x 10 3 3 x x 22. Find the value of x for the following 30° - 60° - 90° triangles. x 10 3 4 3 x x x 8 14 23. Find the vertex, focus, and directrix of the parabola: x 2 6 x 4 y 5 0 9.1 – 9.3 ↓ 24. Find the standard equation of the parabola with its vertex at (2, 1) and its focus at (2, 4). 25. Find the center of the ellipse: 9 x 2 5 y 2 36 x 30 y 36 0 26. a) Find an equation of an ellipse with foci (0, 1) and (4, 1) and major axis of length 6. b) Find an equation of an ellipse with foci (-1, 1) and (-1, 9) and major axis of length 10. 27. Graph: 28. Graph: x 32 25 y2 1 49 y 12 x 42 4 25 1 29. Find the center and foci of the hyperbola: x 2 9 y 2 10 x 18 y 7 0 30. Identify the graph of each conic: 2 x 2 2 y 2 12 x 4 y 9 0 x 2 6x 2 y 9 0 3x 2 6 x 3 y 2 12 y 8 0 4 x 2 y 2 16 x 15 0