How do you solve and find the value of $sin(cos^-1(3/4))$ ?

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Answer 1 · 2017-03-02T10:09:25

$sqrt7/4.$

Let, $cos^-1(3/4)=theta.$

Knowing that, $cos^-1 x=theta iff x=costheta, theta in [0,pi],$ we get,

$costheta=3/4, and, 0 le theta le pi.$

But $costheta >0 rArr theta !in [pi/2,pi] rArr 0 le theta le pi/2.$

$:. sintheta=+-sqrt(1-cos^2theta)=+-sqrt(1-9/16)=+-(sqrt7)/4.$

$0 le theta le pi/2 rArr sin theta gt 0 rArr sin theta=+sqrt7/4.$

$:. sin (cos^-1(3/4))=sintheta=sqrt7/4.$

Enjoy Maths.!

How do you solve and find the value of sin(cos^-1(3/4))sin(cos^-1(3/4))?