i need # 73

Often graphing a function of the form y = A sin x + B cos x is easier by using its reduction formula y = k sin (x + a). For Exercises 67-1 70, a. Use the reduction formula to write the given function as a sine function. b Graph the function. 6\\. y = V3 sin x + cos x Answer 68. y = V2 sin x - V2 cos x 69. y = - sin x + V3 - Cos x 2 Answer 70. y = - VB sin x - - 1 COS X 2 Mixed Exercises 71. a. Is it true that in (2 . 309) = 2 sin 30? Answer b. Expand sin (2 . 309) as sin (30 + 309) using the sum formula for sine. Then simplify the result. Answer 72. a. Is it true that cos (2 . 450) = 2 cos 450? b. Expand cos (2 . 45) as cos ( 45 + 45) using the sum formula for cosine. Then simplify the result. Page 633 73. Derive cos (u + v) = cos u cos v - sin u sin v by using the identity for cos (u - v) and the odd and even function identities for sine and cosine. Answermu (7 For El Exercises tilIE 82, consider a l-kg object oscillating at the end of a horizontal spring. The horizontal positionx (t) of the object is given by W?) = 28in (rut) + 360008 (wt) w 3 2 1 0 1 2 3 where v0 is the initial velocity, )5.) is the initial position, and a) is the number of back-and-forth cycles that the object makes per unit time t. 81. At time t = 0 sec, the object is moved 3 ft to the left of the equilibrium position and then given a velocity of 4 ft/sec to the right (w) = 4ft/sec). V . a. If the object completes 1 cycle in 1 sec (to = 1), write a model of the form x (t) = 0 s1n (cot) + x0003 (wt) to represent the a) horizontal motion of the spring. b. Use the reduction formula to write the function in part (a) in the form x (t) = k sin (I + a). Round 0: to 2 decimal places. c. What is the maximum displacement of the object from its equilibrium position? Technology Connections 101. :1. Graph y = cos (x + g) cos (x g) on the interval [0, 27:]. What simpler function y = f ()6) does this graph appear to represent