Pre-Calc Homework Solutions 34

Pre-Calc Homework Solutions 34 - 34 Section 1.6 82 8 17 21....

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Unformatted text preview: 34 Section 1.6 82 8 17 21. Note that Since sin cos 1 152 and 17. 2 2 29. The solutions in the interval 0 , 2 x 2 are x 7 and 6 x 15 . 17 11 . Since y 6 sin x has period 2 , the solutions are 7 6 sin2 8 , 17 15 , 8 1 cos 8 17 15 , 17 all of the form x sin cos 8 , 15 2k or x 11 6 2k , where k Therefore: sin cot 1 tan tan 17 , 15 is any integer. 17 8 sec 13. 1 cos csc 1 sin 30. The equation is equivalent to tan x solution in the interval 2 1 1 1, so the 22. Note that Since tan have sin cot csc 52 122 x 2 is tan x is , sin 5/13 5 12/13 12 cos 12 5 sin and cos . 13 13 12 5 , cos , tan 13 13 1 1 12 , sec 5 tan cos 1 13 5 sin and 2 2 , we x tan ( 1) 1 4 . Since the period of y 4 3 4 In summary: 5 , 12 13 , 12 all solutions are of the form x integer. This is equivalent to x integer. 1 7 k , where k is any k , where k is any 31. Let sin cos y x r y 4 , 3 5 4 72 11 cos 1 7 11 . Then 0 sin 1 and cos cos2 1 7 , 11 so 23. Note that r sin cot y r x y 4 , 5 ( 3) cos 3 , 4 2 4 x r r x 2 5. Then: 3 , 5 tan 5 , 3 11 6 11 2 7 2 11 0.771. 9 13 9 , 13 sec csc 2. Then: 24. Note that r sin tan sec y r y x r x ( 2)2 2 2 2 2 2 2 2 2 22 cos 2 2 x r x y 32. Let 1 2 sin 1 1 9 1 . Then 2 2 9 2 13 and sin 88 . 13 so 1 2 2 2 2 2 r y 2 2 2 , cos tan sin sin2 tan 1 sin cos Therefore, 9 88 9/13 88/13 1, cot 2, csc 1, 2 13 0.959. 33. (a) Using a graphing calculator with the sinusoidal regression feature, the equation is y 1.543 sin (2468.635x 0.494) 0.438. 25. The angle tan 1(2.5) equation in the interval 0 x x 1.190 is the solution to this 2 x 2 . Another solution in 2 is tan 1(2.5) 4.332. 4.332. The solutions are [0, 0.01] by [ 2.5, 2.5] 1.190 and x 26. The angle cos 1( 0.7) 2.346 is the solution to this equation in the interval 0 x . Since the cosine function is even, the value cos 1( 0.7) 2.346 is also a solution, so any value of the form cos 1( 0.7) 2k is a solution, where k is an integer. In 2 x 4 the solutions are x cos 1( 0.7) 2 8.629 and x cos 1( 0.7) 4 10.220. 27. This equation is equivalent to sin x the interval 0 x 2 are x 6 1 , 2 (b) The frequency is 2468.635 radians per second, which is equivalent to 2468.635 2 392.9 cycles per second (Hz). The note is a "G." 34. (a) b (c) k 2 12 80 2 6 30 (b) It's half of the difference, so a so the solutions in 5 . 6 1 , so 3 1 3 80 2 30 25. 55 2 (when 8 and x (d) The function should have its minimum at t 28. This equation is equivalent to cos x in the interval 0 x is y cos 1 the solution 1.911. the temperature is 30 F) and its maximum at t (when the temperature is 80 F). The value of h is 2 2 8 Since the cosine function is even, the solutions in the interval x are x 1.911 and x 1.911. 5. Equation: y 25 sin 6 (x 5) 55 ...
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