Question

How to solve sin8x+sin4x=0. I think you use sum to product formula but I'm not sure. Also, there should be sixteen answers i believe..

Answer 1

Sin(8x)=sin(4x+4x)

Answer 2

sin8x+sin4x=0
sin(2(4x))+sin(2(2x))=0

Answer 3

Use double angle formula sin2x = 2sinxcosx

Answer 4

sin(2(4x))+sin(2(2x))=0
2sin(4x)cos(4x)+2sin(2x)cos(2x)=0

Answer 5

can you further reduce that?

Answer 6

Yes!

Answer 7

2sin(2 * 2x)cos(2 * 2x)+2sin(2x)cos(2x)=0

Answer 8

2[sin(2 * 2x)cos(2 * 2x)+sin(2x)cos(2x)]=0

Answer 9

how did you get to that step?
what equation?

Answer 10

To simplify, I used the double angle identity for sin. Sin(2x) = 2sinxcosx. In each situation, I set "x" as either "4x" or "2x".

Answer 11

2[sin(2 * 2x)cos(2 * 2x)+sin(2x)cos(2x)]=0
Divide both sides by 2.
sin(2 * 2x)cos(2 * 2x) + sin(2x)cos(2x) = 0
2sin(2x)cos(2x)cos(2 *2x) + sin(2x)cos(2x) = 0

Factor

sin(2x)cos(2x) * [2cos(2*2x) + 1] = 0

Use cos double angle identity cos(2x) = cos^x-sin^x

sin(2x)cos(2x) * [2cos^x - 2sin^x + 1] = 0

Answer 12

It get's quite complicated, to be honest.

Answer 13

from there what terms would i set equal to zero to solve for my answer in radians?

Answer 14

Keep in mind, the method I'm using here is the COMPLICATED WAY.

Simpler way:

sin(8x)+sin(4x)=0
sin(8x)=-sin(4x)
sin(8x)=sin(-4x)

Solve for x.

Answer 15

how would i solve for x from there?(the easy way)

Answer 16

because we are trying to not use calculators