Question

Solve sin A + sin 2A + sin 3A + sin 4A = 0,
for 0 < A < 180 (0 and 180 inclusive)

Answer 1

I've tried using factor formula but still did not manage to get the answer, not sure if factor formula is the right method

Answer 2

I rearrange to sin 4A + sin 2A + sin 3A + sin A = 0,
and after applying factor formula,
2 sin 3A cos A + 2 sin 2A cos A = 0
2 cos A ( sin 3A + sin 2A) = 0
2 cos A ( sin 5/2 A cos 1/2 A) = 0

Answer 3

@thomaster @Preetha

Answer 4

\(A=0^{\circ}\) is one solution by obsrvation

Answer 5

@HatcrewS you are on the right road to solving it

Answer 6

@welshfella how do I continue from there ? T.T

Answer 7

i think there is an error in your last line

Answer 8

2 cos A ( sin 5/2 A cos 1/2 A) = 0
should be
2 cos A ( 2 sin 5/2 A cos 1/2 A) = 0

now its just a matter of equating the 3 terms to 0

Answer 9

@welshfella oh okay i'll try again thanks!

Answer 10

2 cos A = 0
A = 90 degrees

Answer 11

I solve and got 0, 90, 144, 180 but im still missing 72(answer sheet shows that 72 is one of the answer).

Can someone help me get 72 ?