How do you solve $sin(2theta)+sintheta=0$ on the interval $0<=theta<2pi$ ?

Question

44331 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-27T18:22:30

$theta=0, {2pi}/3, pi or {4pi}/3$

Use $sin(2 theta) = 2 sintheta costheta$

Then factor and solve.

$sin(2 theta) + sintheta =0$

$2 sintheta costheta + sintheta =0$

$sin theta (2cos theta +1) =0$

$sin theta = 0$ $color(white)"sssss"$ or $color(white)"sssss"$ $2 cos theta + 1 =0$ so

$sin theta = 0$ $color(white)"sssss"$ or $color(white)"sssss"$ $cos theta = -1/2$

$theta=0, {2pi}/3, pi or {4pi}/3$

How do you solve sin(2theta)+sintheta=0sin(2theta)+sintheta=0 on the interval 0<=theta<2pi0<=theta<2pi?