Find all solutions of the equation in the interval [0, 2tt). (Enter your answers

Question

Find all solutions of the equation in the interval [0, 2tt). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 3 cos^3 x = 3 cos x Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.) 64 cos^2 x - 16 = 0 Use a graphing utility to approximate the solutions (to three decimal places) of the equation in the interval [0, 2pi). (Enter your answers as a comma-separated list.) 7 csc^2 x + 3.5 cot x - 35 = 0

Explanation / Answer

3.

3cos3x = 3cosx

= 3cosx (1-cos2x) = 0

= 3cosx sin2x = 0

= cosx=0 or sin2x = 0

= x = (2n+1)/2 or n , n= 0,1,2,...

Also cos3x = 4cos3x - 3 cosx

implies that 3cos3x - 3cosx = cos3x - cos3x

4.

64 cos2x - 16 = 0

4cos2x - 1 = 0

cos2x = 1/4

cosx = +/- 1/2

x = 60o, 300o or 120o, 240o

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