Help: Inverse trig (1 Viewer)

[FellowStudent]

Prove that:
a) sin^-1 (x) =cos^-1 (1-x²)^1/2, 0≤ x≤ 1

b) cos^-1 (x)=sin^-1 (1-x²)^1/2, 0≤ x≤ 1

Thank you

 

[pikachu975]

Prove that:
a) sin^-1 (x) =cos^-1 (1-x²)^1/2, 0≤ x≤ 1

b) cos^-1 (x)=sin^-1 (1-x²)^1/2, 0≤ x≤ 1

Thank you

a) let theta = sin^-1 (x)
Draw a triangle and the opposite site of theta is x, and the hypotenuse is 1. Use pythagoras and the adjacent side is 1-x^2.
Then costheta = (1-x^2)/1
theta = cos^-1 (1-x^2)

b) Same thing but make the adjacent side x not the opposite.

 

[integral95]

Another method is using the Pythagorean identities