Find the Exact Value of arcsin(sin(5pi/9))

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The exact value of arcsin(sin(5pi/9)) is determined by recognizing that 5pi/9 corresponds to 100 degrees, which is outside the range of the arcsine function. Since arcsine is defined between -pi/2 and pi/2, the correct approach involves using the sine function's periodic properties. The sine of 5pi/9 is calculated as approximately 0.9848, and the arcsine of this value yields 80 degrees. Thus, the final result is arcsin(sin(5pi/9)) = 80 degrees. Understanding the periodic nature of the sine function is crucial for finding the correct arcsine value.
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1. Find the exact value of the expression arcsin(sin(5pi/9))



2. 5pi/9 = 100 degrees and pi/9 = 20 degrees



3. Tried pi/9 but it is wrong
 
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SO, 5pi/9 is 100 degree. So take sin of that. And do the arc sin of that.
Sin(5pi/9) = .9848

arcsin(.9848) = 80 degrees
 
math_help said:
1. Find the exact value of the expression arcsin(sin(5pi/9))



2. 5pi/9 = 100 degrees and pi/9 = 20 degrees



3. Tried pi/9 but it is wrong

Because sine is periodic, it doesn't have a true "inverse". The usual definition of Arcsine gives a value between -pi/2 and \pi/2. 5\pi/9 is not in that range. Use the facts that sin(x+ 2\pi)= sin(x) and sin(\pi- x)= - sin(x).
 

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