Question

Find all solutions to the equation in the interval [0, 2π).

cos x = sin (2x)

Answer 1

pi/2, 3pi/2
pi/6, pi/2, 5pi/6, 3pi/2
0, pi
0, pi/6, 5pi/6, pi

Answer 2

Those are the options

Answer 3

start with
\[\cos(x)=2\sin(x)\cos(x)\] and solve that one

Answer 4

ok i m trying

Answer 5

\[\cos x=\sin 2x\]

Answer 6

\[\cos x =2\sin x \cos x\]

Answer 7

\[cosx(1-2sinx)=0\]

Answer 8

\[cosx=0=\cos \frac{ \pi }{ 2 }=\cos \frac{ 3\pi }{ 2 }\]

Answer 9

so\[x=\frac{ \pi }{ 2 },\frac{ 3\pi }{ 2 }\]

Answer 10

do the same for\[1-sinx=0\]

Answer 11

yes

Answer 12

except it is \(1-2\sin(x)=0\)

Answer 13

making \(\sin(x)=\frac{1}{2}\) and go from there

Answer 14

ya