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 + tan2x = sinkx +- 1 find cos (x + it). 5. sec x sec2x 6. 6. Find the exact value of sin 285. 7. UTILITY POLE Two wires support a utility pole and form angles a and B 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 = 27 v2 sin 20. Find the distance traveled if the initial velocity is 45 feet per second and the angle is 30. 9. sec2 0 10. Find an expression equivalent to ; tan 0 + cot2 0 tan 0 10. 11. If sin 0 = - on the interval (It , "), find the exact value of tan 20. 11.\f14. 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 62 of a ruby when the angle of incidence is 61 = 50 sin 91 using Snell's Formula : n2, where 712 is the refractive index of a gem. m Refractive Index 1-55 sin 92 Diamond 2.40 Ruby 1.?8 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 .1 9 = M. For what value of cos 6 will the mach number be 1'? 17 5111 . 2 18. Find the exact value ofsin 75. 18. 19. Rewrite sin 126 sin 96 as a sum or difference. 19- 20. Find the exact value of; cos 15 sin 315. 20. Bonus Find sin 46' if a is on the interval (180, 270) and cos 9 : g B