SOLUTION: Find sin^-1 x for the given x. Express your answer as a rational multiple of pi. ranging from pi/2 to 3pi/2. sin^-1 0.5=? how do you solving these kind of problems???

Algebra ->  Trigonometry-basics -> SOLUTION: Find sin^-1 x for the given x. Express your answer as a rational multiple of pi. ranging from pi/2 to 3pi/2. sin^-1 0.5=? how do you solving these kind of problems???       Log On


   

Question 964616: Find sin^-1 x for the given x. Express your answer as a rational multiple of pi. ranging from pi/2 to 3pi/2. sin^-1 0.5=? how do you solving these kind of problems???
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
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%28+300%2C+200%2C+0%2C+10%2C+-1%2C+1%2C+sin%28x%29%2C+y+=+0.5%29+
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.