Answer to Question #177460 in Calculus for Nash

Question

Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than one correct form of each answer.)

5 sin²(x) − 9 sin(x) − 2

Answer 1

$5 sin^2(x) − 9 sin(x) − 2$

let y= sin(x)

$\therefore 5y^2 - 9y-2$

using the quadratic formula we have $y=-{1 \over 5}$ or $2$

so,

$sin(x)= -{1 \over 5}$ or 2

since the value of "sin" is between -1 and +1

then, $sin^{-1}( -{1 \over 5})= -11.53\,degrees$