Question

Find all solutions to the equation.

7 sin^2x - 14 sin x + 2 = -5

Answer 1

Try using a substituion, like u = sinx. That means you're left with a familiar quadratic, which you can rearrange and solve using the quadratic formula or some other quicker method. After you solve for u, you can change u back to being sinx and you have 2 equations for sinx, both of which should be more simple to solve.

Answer 2

\(\bf 7 sin^2(x) - 14 sin(x) + 2 = -5\implies 7 sin^2(x) - 14 sin(x) +7=0
\\ \quad \\
7[{\color{brown}{ [sin(x)]}}^2-2{\color{brown}{ sin(x)}}+1]=0\)

as suggested already, solve like you'd any quadratic

Answer 3

that's a good idea, I know where to go from here. thanks both! @Jesusc @jdoe0001

Answer 4

No problem :)