SOLUTION: Solving an equationon the interval 0 less than or equal to pheta and pheta is less than 2 pi. 2 sin pheta + 3 = 2.

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Question 513993: Solving an equationon the interval 0 less than or equal to pheta and pheta is less than 2 pi. 2 sin pheta + 3 = 2.
Answer by drcole(72) About Me  (Show Source):
You can put this solution on YOUR website!
We have the trigonometric equation:
+2%2Asin%28theta%29+%2B+3+=+2+
We need to solve for theta. First, we solve for sin%28theta%29:
+2%2Asin%28theta%29+=+-1+ (subtract 3 from both sides)
+sin%28theta%29+=+-1%2F2+ (divide both sides by 2)
So we are looking for angles theta between 0 and 2%2Api with a sine of -1%2F2. If you draw a unit circle and measure your angle counterclockwise from the positive x-axis, such an angle will be below the x-axis (since the sine is negative) and make a 30 degree (or pi%2F6 radian) angle with the x-axis (since sin%28pi%2F6%29+=+1%2F2). There are two such angles between 0 and 2%2Api:
pi+%2B+pi%2F6+=+%287%2F6%29%2Api and 2%2Api+-+pi%2F6+=+%2811%2F6%29%2Api
So theta+=+%287%2F6%29%2Api and theta+=+%2811%2F6%29%2Api are your two solutions.