Question

Verify:
sin(2π - α) = -sinα

Answer 1

Do you still need help?

Answer 2

Yup, still new to these.

Answer 3

ok

Answer 4

Expand the left side by using the identity

sin (A + B) = (sin A)(cos B) + (cos A)(sin B)

Answer 5

@workin_daily ? Do you understand?

Answer 6

Yeah I think I can do it now that I know my starting point.

Answer 7

Good, Go ahead! Let me know if you need further assistance.

Answer 8

But shouldn't the plus signs be minus for this problem (in the identity formula for sin)?

Answer 9

Just checking

Answer 10

Nope! What I gave you is correct!

Answer 11

Wait.. So basicly 2π is beta, and it's (Beta + (-alpha)) ?

Answer 12

And that's why the formula keeps the plus?

Answer 13

For your question

sin (A - B) = (sin A)(cos B) - (cos A)(sin B)

You just replace the plus sign with a minus sign.

Answer 14

OH I just realized, that's what you meant earlier when you asked "shouldn't the plus signs be minus for this problem (in the identity formula for sin)?"

Answer 15

That's what I was wondering at first but since the problem started out with it minusing alpha and not beta, if that means it's actually beta + negative alpha

Answer 16

Yes Yes! Sorry, am a bit tired.

Answer 17

Same here ha ha.. so:
\[\sin(2\pi+(-\alpha))=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)\]

beta in the formula being 2π

Answer 18

You're making it too complicated.

sin (A - B) = (sin A)(cos B) - (cos A)(sin B)

Just use this directly to obtain\[\sin (2\pi -\alpha)=\sin (2\pi)\cos \alpha -\cos (2\pi)\sin \alpha \]No w simply simplify this!

Answer 19

How can you use 2π where alpha goes? Then it's all alphas

Answer 20

What?? A is 2 pi and B is alpha. You're taking it way too literally! Just simplify and you'll see.

Answer 21

When this equation was covered in class we were using it for exact value, so we found alpha and beta first as two parts of the original angle (ex: cos(35+45) ) and from there found them as fractions. Then simplify.

Answer 22

Do I need to do something similar here and find alpha as a fraction to simplify? (This problem was not covered in class..)

Answer 23

No. Tell me this\[\sin (2\pi)=?\]and\[\cos (2\pi)=?\]

Answer 24

oh haha
sin(2π)= 0
cos(2π)= 1

Answer 25

Yes, do you understand now?

Answer 26

\[=(0)(\cos \alpha)-(1)(\sin \alpha)\]

Answer 27

\[=(\cos \alpha)-(1)(\sin \alpha)\]

Answer 28

Excuse me?? (0)(cos α) = cos α ????? That would imply that (0)(2) = 2, for example. Did someone change the rules while I was sleeping? LOL

Answer 29

Woops haha

Answer 30

OK so you understand?

Answer 31

Yeah I get it, was just having one of those "no brain" moments lol

Answer 32

Thanks for the help!

Answer 33

No problem.

Answer 34

Thanks for the medal although I'm not entirely sure I deserve that one since I was half a sleep. LOL

Answer 35

Still better than my teacher's lecture lol

Answer 36

Thanks. let me know if you need anything else. I'll be online for another half of an hour.

Answer 37

Alight sounds good, thanks