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Find all values of theta in the interval 0° < theta < 360° that satisfy the equation--->
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# Find all values of theta in the interval 0° < theta < 360° that satisfy the equation--->

[From: ] [author: ] [Date: 11-04-26] [Hit: ]
the solutions are t = pi, pi/3 or 5*pi/3.In degrees,t = 180 degrees,......
sine 2theta = sine theta

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sin(2t) = sin(t), where 0 < t < 360 degrees

Using the result: sin(2t) = 2sin(t)cos(t), we have

2sin(t)cos(t) = sin(t)
=> 2sin(t)cos(t) - sin(t) = 0
=> sin(t)(2*cos(t) - 1) = 0
=> sin(t) = 0 or cos(t) = 1/2

In the closed interval [0, 2*pi],

sin(t) = 0 for t = 0, pi and 2*pi
cos(t) = 1/2 for t = pi/3 and 5*pi/3

For the open interval (0, 2*pi), the solutions are t = pi, pi/3 or 5*pi/3.
In degrees, that corresponds to:

t = 180 degrees, 60 degrees or 300 degrees
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