How do you solve $sin theta= -0.5$ ?

Question

15577 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-19T02:04:53

$(7pi)/6 + pi * k$ , where k is all integers.

If they are asking the value on $theta$ on the interval $0 <= theta <= 2pi$ the solutions are: $(7pi)/6 and (11pi)/6$

$sin(theta) = -0.5$
$sin(theta) = -1/2$

Looking at the unit circle, $sin(theta) = -1/2$ at $(7pi)/6 and (11pi)/6$ but since sine is periodic every $2pi$ the solutions are:

$(7pi)/6 + pi * k$ , where k is all integers.

Answer 2 · 2018-05-19T02:16:53

$theta = 2n pi - pi/6, 2npi - (5pi)/6$ , n $1 in ZZ$

$sin theta = -0.5$

$sin theta = sin (-pi/6)$

$theta = -pi/6$

Generalising

$theta = 2n pi - pi/6, 2npi - (5pi)/6$ , n $1 in ZZ$

How do you solve sin theta= -0.5 sin theta= -0.5 ?