Question

Solve for x: sin2x=sin x, 0≤x≤2π

Answer 1

Youd have to use an identity on the sin2x. Because you cant have different angles when youre solving these. SO you usr a double angle formul on sin2x to get everything int erms of just a single x angle. Do you know the double angle identity for sin2x?

Answer 2

No sorry

Answer 3

Well, a lot of these you may be forced to remember unfortunately, so might as well write them down when they come up. So, sin2x = 2sinxcosx. Meaning youre actually trying to solve
2sinxcosx = sinx

Answer 4

So using that formula the equation will become 2sinxcosx=sinx then divide both sides by sinx which will leave you with sinxcosx as your answer

Answer 5

Well first off if you divide both sides by sinx you have 2cosx = 1. But even then you still have more work to do. You cant just solve for cosx or sinx, you have to solve for the actual x.

Answer 6

So what we need to do is get the cosx by itself, just as if we were solving for x. So that means I also want to divide both sides by 2 to give us

cosx = 1/2

Now, do you have a unit circle chart handy?

Answer 7

Yes

Answer 8

Alright, cool. So there are two angles on the unit circle where cosx = 1/2. Just gotta find them.

Answer 9

Okay is it (cos, sin) on the unit circle

Answer 10

Yes, cos is x, sin is y

Answer 11

Okay so the angle would be 60

Answer 12

thats one of the 2.

Answer 13

Okay and the other is 300

Answer 14

Yep, those are your two answers then :3

Answer 15

So do you just write is as x=300 and 60 degrees

Answer 16

Pretty much.

Answer 17

Thank you so much!

Answer 18

Yeah. np ^_^