Question

Helpful steps please,
Solve the equation in the interval [0°,360°].
sin 2(theta) = -sin(theta)

Answer 1

use the identity
sin 2(theta) = 2 sin(theta) cos(theta)

Answer 2

I'm still stuck I'm not sure how to progress using that identity.

Answer 3

i'll write x instead of theta right as I am a bit lazy!

2 sin x cos x = - sin x
add sin x to both sides

2 sin x cos x + sin x = 0

now you can factor the left hand side , then its easy

Answer 4

would it then be 0,120,180,240 ?

Answer 5

sin x(2 cos x + 1 ) = 0
so
sin x = 0 or 2cos x + 1 = 0

sin x = 0 or cos x = -1/2

Answer 6

for sin x = 0
x = 0, 180,360

for cos x = -1/2

x is in the 2nd and 3rd quadrants

Answer 7

ok so cos=-1/2 x would be 60,120,240,300
but for sin x=0 they only have 0 and 180 not 360 for the set of solutions

Answer 8

the interval is [0 degrees, 360 degrees) *

Answer 9

no cos is negative only in the 2nd and 3rd quadrants its 120 and 240 only

Answer 10

no 360 is a solution the squared brackets means you include 360

Answer 11

- oh it looks like ] to me

Answer 12

my mistake I naturally did the " ]" instead of " )" by habit

Answer 13

but if its ) then yes - no 360

Answer 14

so 0,120,180,240 is the correct solution

Answer 15

ah thanks!

Answer 16

yw

Answer 17

hace you seen this memory aid