what are all the solutions of 5sin(theta)-4=2sin(theta)-4

Question

p0sitr0n · Answer

replace sin theta by x and solve

solomonzelman · Answer

$$5Sinx-4=2Sinx-4$$let Sinx=a$$Sinx=a$$
$$5Sinx-4=2Sinx-4$$$$5Sinx=2Sinx$$

solomonzelman · Answer

$$Sinx=0$$$$x=?$$

solomonzelman · Answer

I'll tell you this rule.$$Sinx=0~~~~~~~~~~~x=0$$

solomonzelman · Answer

Do you get it?

anonymous · Answer

I don't understand what to do with the 5 and the 2

solomonzelman · Answer

Are you clear till$$5~Sinx=2~Sinx$$

anonymous · Answer

yes

solomonzelman · Answer

So now the "COMMON SENSE"  comes to rescue.

$$5~Sinx=2~Sinx$$let  Sin x  =  number    OR  let  Sinx=a
$$5a=2a$$this can only be true when a=0, so$$Sin~x=0$$

anonymous · Answer

what about pi?

solomonzelman · Answer

pi?

anonymous · Answer

in my work sheet the is 0, 2pi, pi  or 0 ,
2pi

solomonzelman · Answer

read what you wrote please.

anonymous · Answer

like the options are:
a. 0, 2pi, pi
b. 0, pi

solomonzelman · Answer

Oh, OK.

solomonzelman · Answer

well looking over the work, you can clearly see that    Sin x=0   must be true.

So your answer would be $$Sin^{-1}0$$which is ZERO.

it's not pi or anything like that.

anonymous · Answer

thank you

solomonzelman · Answer

Anytime, I'm not good at math, but tried my best.

anonymous · Answer

Actually, the answer would be 2pi*k...where k is any integer. Think of all of the infinite possibilities when co-terminal angles come to mind.