Question 964616
sin^-1 0.5 = ?
This problem is asking you to calculate the inverse sign function for 0.5, the answer can be in degrees or radians.  If your teacher allows you to use a calculator, then look for the sin^-1 function.  Sometimes the calculator will have an inverse function that applies to trig functions.
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sin^-1 0.5 = 30 degrees, which implies that sin 30 = 0.5
note that 30 degrees is not the only answer, since trig functions have a period of 360 degrees.
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We are asked to evaluate sin^-1 0.5 over pi/2 to 3pi/2.  Note that pi is 180 degrees for trig functions, therefore
we evaluate sin^-1 0.5 from 90 degrees to 270 degrees
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sin 150 = 0.5, 
note sin 210 = -0.5
therefore between 90 degrees and 270 degrees, we have one answer sin 150 = 0.5
now we need to convert 150 to a rational multiple of pi (180)
150 / 180 = 5pi / 6
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consider the graph of the sin function
{{{ graph( 300, 200, 0, 10, -1, 1, sin(x), y = 0.5) }}}
The minimum of the first dip below the x-axis corresponds to 270 degrees and the first maximum above the x-axis corresponds to 90 degrees.  Now the values on the y-axis range over +1 to -1, so if you draw a line (green line) parallel to the x-axis half way between 0 and 1 (0.5), you see that there is just one positive value between 90 and 270 degrees.