Find the exact value of each expression Remember to show you

Find the exact value of each expression (Remember to show your work. This is not a calculator problem, so answers should be exact.)

sin(tan^-1 (sqrt7))

Let x = tan^-1 (sqrt7)

tanx = sqrt7

So, hypotenuse = sqrt( 7 +1) = 2sqrt2

sinx = sqrt(7)/2sqrt2

x = sin^-1{sqrt(7)/2sqrt2}

sin(tan^-1 (sqrt7)) = sinx = sin{sin^-1{sqrt(7)/2sqrt2}

= sqrt7/2 *sqrt2