Question

FInd all x, 0 less than or equal to x less than or equal to 2pi, such that 3cos^2x + 4sin x = 4.

Please explain! :)

Answer 1

start with the fact that \(\cos^2(x)=1-\sin^2(x)\) to get a quadratic equation in sine

Answer 2

\[3\cos^2(x) + 4\sin(x) = 4\]
\[3(1-\sin^2(x))+4\sin(x)-4=0\]
\[3-3\sin^2(x)+4\sin(x)-4=0\]
\[-3\sin^2(x)+4\sin(x)-1=0\] or maybe
\[3\sin^2(x)-4\sin(x)+1=0\] then solve the quadratic equation

Answer 3

what do you mean by "or maybe"?

Answer 4

reverse all the signs in the quadratic

Answer 5

ok...

Answer 6

if you want to do that you can

Answer 7

k, thanks:)