## Darion 3 years ago Can someone help me please? Rewrite with only sin x and cos x. cos 2x + sin x

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1. Schrodinger

Okay. So this stems from trigonometric identities and double angle formulas. Do you know any double angle formulas?

2. Darion

Not really, no. Sorry

3. Schrodinger

No prolem. A really good reference for all of these formulas would be this: (one minute.)

4. Schrodinger

*No problem. Anyways, here's the webpage with pretty much every possible identity you can imagine for Trig. http://www.sosmath.com/trig/Trig5/trig5/trig5.html You'll notice that under the double angle formulas section, Cos(2x) has three different accompanying equations. Can I ask what math you're in right now, i'm assuming Precalc?

5. Darion

You are correct, I'm in precalc. And thanks for the link btw. That is awesome.

6. Schrodinger

$\cos(2x) = \cos ^{2}(x) - \sin ^{2}(x)$$\cos(2x) = 2\cos ^{2}(x)-1$$\cos(2x) = 1 - 2\sin ^{2}(x)$

7. Schrodinger

No problem. Okay, given these formulas, we can substitute cos(2x) for other things without double angles. Right now, we've got $\cos(2x) + \sin(x)$, correct?

8. Darion

Yes

9. Schrodinger

(Sorry for asking something you obviously know the answer to, just giving myself time to think LOL. I haven't done this in a while.)

10. Darion

No you're doing great. You're helping me way more than anyone has thus far. Take all the time you need I really appreciate your helping me out man.

11. Schrodinger

No worries. I'm a little confused about the vague instructions. While you can rewrite it with those terms, i'm wondering if it's acceptable to have only sine, only cosine, or whether cosine or sine squared is acceptable. After all, that is basically what these are. Guess every case might be worked out.

12. Darion

If it helps, the possible answers are: 1 + 3 sin x 1 + 3 sin2x 1 - 2 sin2x + sin x 1 + 2 sin2x + sin x

13. Darion

The last 3 are (sin^2 x) btw

14. Schrodinger

Oh, lol, okay then. That's WAY simpler than what I was about to do. My bad, I was like, half-trying to solve a trig identity. So yeah, just take a look at the formulas I put up, and substitute them. From there it's super easy to see which one makes sense with the possible answers.

15. Schrodinger

Don't try to solve anything, just see which substitution would get you closest to the answers given. It should be a single step.

16. Schrodinger

You follow?

17. Darion

I think so. So the answer would just be 1 - 2 sin2x + sin x

18. Schrodinger

Exactly, but I have to say, don't be afraid of using the carat symbol (^) if you're ever writing something on a computer and can't put in a fancy superscript like: $\sin ^{2}x$ to denote when a value is squared. People could very, very easily misread it as sin(2x) instead of sin^2(x), and that could mess up a whole problem.

19. Darion

Thanks for the tip and all your help. I can't thank you enough.

20. Schrodinger

No problem. Good luck with Precalc. I struggled a lot with it when I first learned it.

21. Schrodinger

(Heck, i'm still learning it, albeit different forms.)

22. Darion

Haha. I guess it never really ends does it?

23. Schrodinger

Nope. We're dumb forever. :P PS, I don't know if this would apply to you, but do you use flash cards to study?

24. Darion

sometimes. I guess it depends on what I am studying. If there are a lot of vocabulary words or something I will usually use flashcards.