Find the exact value of each expression Do not use calculato

Find the exact value of each expression. Do not use calculator.

Find the exact value of each expression. sin [tan^-1(-1)]

Solution

given sin( arc tan(1) )

first let us say arc tan1 =x

1 = tan(x)

tan(x) =1 , then x =pi/4

so sin( arc tan(1) ) becomes sin(x)

but x=pi/4

so the expression becomes sin(pi/4) = 1/sqrt(2)

the final answer is 1/sqrt(2) [ sqrt is square root of ]