Question

find the intersection of the following graphs over the interval [0,2pi).
f(x)=sin2x
g(x)=cosx

Answer 1

@jdoe0001 do i set them equal to each other?

Answer 2

solve f(x)=g(x) for x
that is solve sin(2x)=cos(x)
use double angle identity for sin(2x)

Answer 3

yeap, you set f(x) = g(x)
whatever value "x" gets, is where they intersect

Answer 4

be wary of cancelling cosine in the simplification, btw

Answer 5

ok so does it look like 2sinxcosx=cox

Answer 6

how do i simplify that down further?

Answer 7

so.... \(\begin{array}{llll}
f(x)=sin(2x)\\
g(x)=cos(x)
\end{array}\implies sin(2x)=cos(x)
\\ \quad \\
{\color{brown}{ 2sin(x)cos(x) }}=cos(x)\implies
2sin(x)cos(x)-cos(x)=0
\\ \quad \\
cos(x)[2sin(x)-1]=0\implies
\begin{cases}
cos(x)=0\implies &x=cos^{-1}(0)\\
2sin(x)-1=0\implies &x=sin^{-1}\left( \frac{1}{2} \right)
\end{cases}\)

Answer 8

ohhhh thanks!

Answer 9

you could have cancelled cosine in the simplification, instead of doing common factor
but you'd have lost a valid value in the process
tis what I meant, be wary of cancelling it :)