Question 1102807: An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
2 sin(3θ) − 1 = 0
Find the solutions in the interval
[0, 2π). Thank you!
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
We are to find all the solutions for x of the equation 2 sin(3x) - 1 = 0 in the interval [0, 2pi). The first thing we should note is that if x is in the interval [0, 2pi) then 3x is in the interval [0, 6pi).
The solutions for 3x on the interval [0, 6pi) are
pi/6, 5pi/6, 13pi/6, 17pi/6, 25pi/6, and 29pi/6
The solutions for x on the interval [0,2pi) are
pi/18, 5pi/18, 13pi/18, 17pi/18, 25pi/18, and 29pi/18
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