Question
Solve for theta.
6 sin theta-1=2 sin theta +1
0 ≤ theta < 2 pi
Please show the work as equations. Give the exact radian measure and no decimals.
6 sin theta-1=2 sin theta +1
0 ≤ theta < 2 pi
Please show the work as equations. Give the exact radian measure and no decimals.
Answers
We can solve this equation by isolating the sine function on one side and using trigonometric identities to simplify it:
6 sin theta - 1 = 2 sin theta + 1
4 sin theta = 2
sin theta = 1/2
This means that theta could be in either the first or second quadrant (where sine is positive), and the reference angle for theta is pi/6. Therefore, the solutions are:
theta = pi/6 or theta = 5pi/6
If we add multiples of 2pi to these values, we can get all possible solutions in the given interval of 0 ≤ theta < 2 pi. Therefore, the solutions are:
theta = pi/6 + 2npi or theta = 5pi/6 + 2npi, where n is an integer.
6 sin theta - 1 = 2 sin theta + 1
4 sin theta = 2
sin theta = 1/2
This means that theta could be in either the first or second quadrant (where sine is positive), and the reference angle for theta is pi/6. Therefore, the solutions are:
theta = pi/6 or theta = 5pi/6
If we add multiples of 2pi to these values, we can get all possible solutions in the given interval of 0 ≤ theta < 2 pi. Therefore, the solutions are:
theta = pi/6 + 2npi or theta = 5pi/6 + 2npi, where n is an integer.
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