Question

Find all the solutions for theta, given 0< or equal to theta < 2pi, for the function Sin 2(theta)-Cos(theta) = 0

Answer 1

cos(theta)=0 or sin(theta)=(1/2)

Answer 2

start with \(\sin(2x)=2\sin(x)\cos(x)\)

Answer 3

theta=pi/2, 3pi/2, pi/6, 5pi/6

Answer 4

then
\[2\sin(\theta)\cos(\theta)-\cos(\theta)=0\]
\[\cos(\theta)(2\sin(\theta)-1)=0\]
\[\cos(\theta)=0\iff \theta =\frac{\pi}{2},\text{ or } \theta =\frac{3\pi}{2}\]

Answer 5

or
\[2\sin(\theta)-1=0\]
\[\sin(\theta)=\frac{1}{2}\] what @josiahh sais

Answer 6

Thanks guys