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.!