Is it possible for x to be negative in the equation arcsin x + arcsin 2x = pi/2?

[Michael_Light]

Homework Statement

sin ^-1x + sin ^-12x = ∏/2

Homework Equations

The Attempt at a Solution

My question is, is it possible for x to be a negative value? Since ∏/2 is positive. Or I should think that x can be negative because -(3∏)/2 = ∏/2?

Please enlighten me...
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[SammyS]

sin^-1(x) has the same sign as x , so the answer to your question is "No, that's not possible."

 

[ehild]

-3pi/2 is not equal to pi/2, but the angle -3pi/2 is equivalent to the angle pi/2.

The range of the inverse sine function is [-pi/2,pi/2]. -3pi/2 is outside of the range.

Hints to solve the problem:

sin(sin^-1(x))=x.

sin(pi/2-α)=cosα.

What is cos(sin^-1(x))?

ehild