Chapter 5 Test, Form 2C SCORE 1. Simplify (sec 0 - tan 0)(1 + sin 0). 1. 2. If tan 0 = - - on the interval (90, 1809), find sec 0. 2. 3. SCIENCE The amount of force needed to keep a stationary object on a flat surface from moving is called static friction. If a book weighs p pounds and it is on a flat surface that is at an angle of 0 degrees, the coefficient of static friction c for the book is given by cp cos 0 = p sin 0. Solve the equation for c and find the value of c when 0 = 450. 3. 4. Simplify sin 0 + cos 0 tan 0. 4. 5. If 1 + tan' x - = sin2x + - find cos (x + n). 5. sec x sec2x 6. 6. Find the exact value of sin 2850. 7. UTILITY POLE Two wires support a utility pole and form angles a and f with the ground. Find the value of sin (a - B) if cos a = on the interval (0, 909) and cot B = on the interval (0, 90). 7. 8. Simplify cos (" -0). 8. 9. SOCCER The horizontal distance x traveled by a soccer ball if it is kicked from ground level with an initial velocity of vo and angle 0 is x = = v2sin 20. Find the distance traveled if the initial velocity is 45 feet per second and the angle is 30. 9. 10. Find an expression equivalent to; sec2 0 10. tan 0 + cot2 0 tan 0 11. If sin 0 = - = on the interval (It, " ), find the exact value of tan 20. 11. 12. If sin 0 = 0.9, find- 1 12. sin (8 - ") 13. Solve 2 sin x + 1 = 0 on the interval [0, 2nt). 13.Chapter 5 TeSt, Form 2C (continued) 14. The refractive index of a gem helps account for its brilliance as light passes through air and bends as it enters the gem. The refractive index of several gems is listed in the table. Find the approximate refraction angle 92 of a ruby when the angle of incidence is 91 = 50 sin 91 using Snell's Formula : n2, where n2 is the refractive index of a gem. sin 32 Refractive Index Amber 1.55 Diamond 2.40 Ruby 1.78 Sapphire 1.77 14. 15. Solve 2 cos x sinzx + 2 = 0 for all values ofx. 15' 16. Solve cos E : sin x on the interval [0, 21:). 16. 17. MACH NUMBER The angle 6 at the vertex of the cone-shaped shock wave produced by a plane breaking the sound barrier is related to the mach number M describing the plane's speed by the equation % = M. For what value ofcos 8 will the mach number be 1'? 1? sm 3 . l8. Find the exact value of sin 75. '8- 19. Rewrite sin 120 sin 90 as a sum or difference. 19. 20. Find the exact value of; cos 15 sin 315. 20, Bonus Find sin 46 it'd is on the interval (180, 2T0) and cos :9 : E. B