SOLUTION: Tan(sin^-1(-3/8)

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Question 1039100: Tan(sin^-1(-3/8)
Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
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Tan(sin^-1(-3/8)
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You want to find tan%28arcsin%28-3%2F8%29%29.

Let alpha be arcsin%28-3%2F8%29: alpha = arcsin%28-3%2F8%29.

Then  alpha  is in  Q4  and +sin%28alpha%29 = -3%2F8.

In this case,  cos%28alpha%29 = sqrt%281-%28-3%2F8%29%5E2%29 = sqrt%281-9%2F64%29 = sqrt%2855%29%2F8.

Notice that  cos%28alpha%29  is positive in  Q4.

Hence,  tan%28alpha%29 = sin%28alpha%29%2Fcos%28alpha%29 = %28%28-3%2F8%29%29%2F%28%28sqrt%2855%29%2F8%29%29 = -3%2Fsqrt%2855%29 = -%283%2Asqrt%2855%29%29%2F55.

Solved.

For more similar problems see the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.