How do you evaluate $sin (cos^-1 (sqrt 2/2))$ ?

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Answer 1 · 2018-06-26T06:20:17

$sqrt2/2$

$cos(x)=sqrt2/2$ at $pi/4$ radians therefore $cos(pi/4)=sqrt2/2$

$cos^-1(cos(pi/4))=cos^-1(sqrt2/2) rarr pi/4=cos^-1(sqrt2/2)$

Sub this into original equation

$sin(cos^-1(sqrt2/2)) rarr sin(pi/4)$

$sin(pi/4)=sqrt2/2$

How do you evaluate sin (cos^-1 (sqrt 2/2))sin (cos^-1 (sqrt 2/2))?