# math(Trigonometry)

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sin 2 theta + cos theta = 0

so, we use sin 2 theta = 2 sin theta cos theta right? but the problem is i'm stuck on (2 sin theta cos theta) + cos theta = 0. What should i do?

• math(Trigonometry) -

cosTheta(2SinTheta+1)=0

remember ab=o? a or b or both is = zero

• math(Trigonometry) -

i see you factorised the question. But, still i can't find the solution. but how about this:

2sin theta cos theta = - cos theta
2sin theta = - cos theta/cos theta
2sin theta = -1
sin theta = -1/2
theta = sin^-1(1/2)
theta = 30

• math(Trigonometry) -

from Bob's , cosØ(2sinØ + 1)=0
cosØ = 0 or sinØ = -1/2

if cosØ = 0, then Ø = 90° or 270° OR Ø = π/2 , 3π/2

if sinØ = -1/2, Ø must be in III or IV
Ø = 180+30 = 210° or 360-30 = 330°
in radians Ø = 7π/6 , 11π/6

you totally ignored the fact it was -1/2
and did not take the CAST rule into consideration.

• math(Trigonometry) -

Yeah, usually i used sinØ = -1/2 to find the quarters and skipped the negative to find theta.

"if sinØ = -1/2, Ø must be in III or IV. Hence, Ø = 180+30 = 210° or 360-30 = 330°"

However, i got the same answers as yours :). Just to make sure whether it is correct or not.
Thanks for the guide bobpursley and Reiny!

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