Question

Solve the equation for all t ∈ [0, 2π)

sin 2x + 2 cos x + √3 sin x + √3 = 0

Give the exact sum of the solutions found above.

Answer 1

sin 2x + 2 cos x + √3 sin x + √3 = 0
2sin x cos x + 2 cos x + √3 sin x + √3 = 0
2cosx (sinx +1) + √3 ( sinx +1) =0
( 2cosx + √3) (sin x +1) =0
( 2cosx + √3) =0 or (sin x +1) =0
cosx = -√3 /2 or sin x =-1
Can you solve them from here?

Answer 2

@shelovespiano ?

Answer 3

I'm trying to figure this out, i guess... I haven't been taught this and we were expected to figure it out from the book's description.

So, from there you'd take the arccos and arcsin then?
Or just check a chart?

Answer 4

Either of them will do, since they are the special angles

Answer 5

ok, thanks!

Answer 6

Could you explain how you got from step three to step 4 please?

Answer 7

cosx = -√3 /2
x = 180 - 30 =? or x = 180 + 30 =?

sin x =-1
x = 270

Put the angle back to the equation to check if it satisfies the equation

Answer 8

Do factorization, there is a common factor (sinx+1) in the 2 terms

Answer 9

OH, I see now. thanks again!

Answer 10

Welcome :)