Question

Giving medals!!!
Find all solutions to the equation.
7 sin2x - 14 sin x + 2 = -5

Answer 1

\(7sin^2(x)-14sin(x)+2=-5\) ?

Answer 2

yeah

Answer 3

First, we like to transpose -5 to the left:
\(7sin^2(x)-14sin(x)+7=0\)
Then factor out the value 7, and hence simplify the equation:
\(sin^2(x)-2sin(x)+1=0\)
Substitute u=sin(x) to reduce the problem to a quadratic:
\(u^2-2u+1=0\)
Factorize expression on the left:
\((u-1)^2=0\)
that gives a solution of u=1
which means sin(x)=1.
Can you solve this equation (completely) now?

Answer 4

yes thats exactly what I needed! thanks!

Answer 5

You're welcome! :)