Question 1 of 18, Step 1 of 1 Correct ies, algebraic methods, and inverse trigon

Question

Question 1 of 18, Step 1 of 1 Correct ies, algebraic methods, and inverse trigonometric functions, as necessary, to solve the following trigonometric equation on the interval [0. 2x) Round your answer to four decimal places, if necessary. If there is no solution, indicate "No Solution." 2cos(2x) - 6cos(x) 2 0 Answer How to enter your answer Enter your answer in radians, as an exact answer when possible. Multiple solutions should be separated by commas. Keypad l replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used O No Solution Submit Answer 2018 Hawkes Learning 11:50 AM

Explanation / Answer

2 cos 2x - 6 cos x - 2 = 0

cos 2 x = 2 cos^2 x -1

2 ( 2 cos^2 x -1 ) - 6 cos x - 2 = 0

4 cos^2 x - 6 cos x - 4 = 0

( cos x - 2 ) ( 2 cos x + 1 ) = 0

cos x = 2 , cos x = -1/2

x = 2pi/3 , 4pi/3

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