`sec(sin^-1 (-sqrt(2)/2))` Find the exact value of the expression. (Hint: Sketch a right triangle.)

kspcr111 | Student

`sec(sin^-1 (-sqrt(2)/2))`

`Let theta = sin^-1 (-sqrt(2)/2)`

so we need to find `sec (theta)`

=> `sin(theta) = (-sqrt(2)/2)`

=>` sin(theta) = -1/sqrt(2)`

we know

`sin^2(theta) +cos^2(theta) = 1`

=>` (-1/sqrt(2))^2 + cos^2(theta) = 1`

=>` (1/2)+cos^2(theta) = 1`

=> `cos^2(theta) = 1-1/2 =1/2`

=>` cos(theta) = 1/(sqrt(2))`

so , `sec(theta) = sqrt(2)`