arcsin x + arcsin 2x = pi/2

Michael_Light

1. The problem statement, all variables and given/known data

sin ^-1x + sin ^-12x = ∏/2

2. Relevant equations

3. 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...
[

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

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Michael_Light	arcsin x + arcsin 2x = pi/2 Tweet 1. The problem statement, all variables and given/known data sin ^-1x + sin ^-12x = ∏/2 2. Relevant equations 3. 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... [

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

ehild Recognitions: Homework Help	-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