How do you solve $sin 2theta - cos theta = 0$ between 0 and 2pi?

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Answer 1 · 2016-02-15T08:43:05

in Degrees: $" " " "theta=30^@, 90^@, 150^@, 270^@$
in Radians: $" " " "theta=pi/6, pi/2, (5pi)/6, (3pi)/2$

The given: Solve
$sin 2theta-cos theta=0$

because
$sin 2theta=2*sin theta cos theta$
it follows

$2 sin theta cos theta-cos theta=0$
factor out $cos theta$

$cos theta(2 sin theta-1)=0$
Equate both factors to zero

$cos theta=0$ and $2 sin theta-1=0$
$theta=cos^-1 (0)=90^@, 270^@$

also

$2 sin theta = 1$
$sin theta = 1/2$
$theta=sin^-1 (1/2)=30^@,150^@$

the solutions are:

$theta=30^@, 90^@, 150^@, 270^@$

have a nice day...from the Philippines !

How do you solve sin 2theta - cos theta = 0 sin 2theta - cos theta = 0 between 0 and 2pi?