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Homework Statement
y = -2sin2(x+[pi/6])+1 for x [-pi, pi]
The Attempt at a Solution
set y=0,
1/2 = sin2(x+[pi/6])
pi/6 = 2(x+[pi/6]), where pi/6 is the base angle
Now because of the 2 infront of the (x+[pi/6]), I consider twice the domain, i.e. [-2pi, 2pi].
pi/6 is positive, and sin is positive in 1 & 2 quadrants.
therefore,
2(x+[pi/6]) = pi/6, 5pi/6, -7pi/6, -11pi/6.
divide by 2:
(x+[pi/6]) = pi/12, 5pi/12, -7pi/12, -11pi/12.
subtract [pi/6] from both sides:
x = -pi/12, 3pi/12, -9pi/12, -13pi/12.
This is my problem. Is -13pi/12 an issue since it is outside the original domain, or is it still ok since it is inside the modified domain [-2pi,pi]?
the answer has x values of -pi/12, 3pi/12, -9pi/12, 11pi/12, so my only issue is the last value. What has gone wrong!?