Finding the angle from sin(2 theta)=0.348

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To find the second angle for sin(2θ) = 0.348, the first angle is identified as 10.2 degrees. The confusion arises regarding the calculation of the second angle, with one suggestion being 180 - (2 * 10.2), while the book states it should be 90 - 10.2. The correct approach involves recognizing that if x = 2θ, then x can equal 20.4 degrees or 180 - 20.4 degrees. Ultimately, the second angle is derived by converting x back to θ and solving accordingly. Understanding the properties of the sine function and the angle transformations is crucial in this context.
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I was wonder how to find the second angle to this problem. I already know one of the angle is 10.2 degree but shouldn't the the second angle be 180-(2*10.2) since in the second quadrant, sin values are positive but in the book, it's given as 90-10.2. Is it something to do with the properties of (2 theta)?
 
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maiad said:
I was wonder how to find the second angle to this problem. I already know one of the angle is 10.2 degree but shouldn't the the second angle be 180-(2*10.2) since in the second quadrant, sin values are positive but in the book, it's given as 90-10.2. Is it something to do with the properties of (2 theta)?
Let x=2θ. Then you have sin x = 0.348, so x=20.4 or x=180-20.4. Now write x in terms of θ and solve.
 
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