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# Help on C3 trigonometry please? Tweet

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1. Help on C3 trigonometry please?
Can someone please explain something to me.

I know the addition formula required for this question but I dont understand how they got to the answer. Sorry im not sure how to draw the theta sign on here so I've just written the word.

The question is:

Express the following as a single sine, cosine or tangent: Cos2theta costheta + sine2theta sinetheta.

The answer is cos theta but Im not sure why. I assumed it was cos theta + sin theta.

Does anyone know how to get rid of the sin theta?

Thank you
2. Re: Help on C3 trigonometry please?
think of this as just the expansion for "Cos(2theta-theta)" - try expanding THAT and see if you get the same
3. Re: Help on C3 trigonometry please?
I got 2costheta if that helps at all? x
4. Re: Help on C3 trigonometry please?
I got costheta, but I'm new to these forums and I don't know how to use proper symbols (as in formulae and such). I tried to type it but it was unreadable
5. Re: Help on C3 trigonometry please?
(Original post by Hasufel)
think of this as just the expansion for "Cos(2theta-theta)" - try expanding THAT and see if you get the same
Thank you for replying. I think im missing something here. I understand that Cos(2theta - theta) is equal to Cos theta. Im just confused why this isnt the same if you expand sine2theta sinetheta into sine (2theta - theta) to give sinetheta? I cant see it cancelled out :s
6. Re: Help on C3 trigonometry please?
Actually I got cos(theta)

cos2(theta)cost(theta) + sin2(theta)sin(theta)

cos2theta = 2cos^2-1 and sin2theta = 2sinthetacostheta

I am going to call theta x for ease

so it = (2cosx^2-1)cosx + 2sinxcosxsinx
= 2cos^3 - cos x + 2sinx^2cos x
= 2 cosx^ 3 - cos x + 2(1-cosx^2)(cos x)
= 2cos x ^3 - cos x + 2cos x - 2 cos x^ 3
= cos x
7. Re: Help on C3 trigonometry please?
Ahh thanks for trying! Is it possible to just type it anyway please? I would rather take time making sense of it than still not being able to figure it out. However if its long winded and time consuming for you, thanks again
8. Re: Help on C3 trigonometry please?
Haha you're more than welcome, as I didn't help at all! Did it exactly as the user above you, glad someone typed it out clearly
9. Re: Help on C3 trigonometry please?
(Original post by Liquidise.)
Haha you're more than welcome, as I didn't help at all! Did it exactly as the user above you, glad someone typed it out clearly
Is it actually understandable? I wasn't sure :P
10. Re: Help on C3 trigonometry please?
(Original post by Annalouxxxx)
Is it actually understandable? I wasn't sure :P
Haha yeah, it's great, nicely done couldn't figure it out myself how to write it legibly.
11. Re: Help on C3 trigonometry please?
(Original post by Annalouxxxx)
Actually I got cos(theta)

cos2(theta)cost(theta) + sin2(theta)sin(theta)

cos2theta = 2cos^2-1 and sin2theta = 2sinthetacostheta

I am going to call theta x for ease

so it = (2cosx^2-1)cosx + 2sinxcosxsinx
= 2cos^3 - cos x + 2sinx^2cos x
= 2 cosx^ 3 - cos x + 2(1-cosx^2)(cos x)
= 2cos x ^3 - cos x + 2cos x - 2 cos x^ 3
= cos x
Thanks for all the help! It sort of makes sense, i'll break it down and read it thoroughly I just noticed that the next exercise from the textbook deals with 2sintheta being equal to 2sinthetacostheta and other double angle formulae so I wasn’t aware of that particular equation. Rather unfair of them to do that!
12. Re: Help on C3 trigonometry please?
(Original post by amani-puresapphire)
Thanks for all the help! It sort of makes sense, i'll break it down and read it thoroughly I just noticed that the next exercise from the textbook deals with 2sintheta being equal to 2sinthetacostheta and other double angle formulae so I wasn’t aware of that particular equation. Rather unfair of them to do that!
That is mean! If you're stuck on any part just message me x
13. Re: Help on C3 trigonometry please?
(Original post by Annalouxxxx)
That is mean! If you're stuck on any part just message me x
Ahh I got it! I am so grateful. Between the equations for the exercise I was working on and the next, I put it all together. Trig will be the end of me I will take you up on that offer without being a pest hopefully. Self teaching myself A2 maths is troublesome. I do love the student room though
14. Re: Help on C3 trigonometry please?
(Original post by amani-puresapphire)
Ahh I got it! I am so grateful. Between the equations for the exercise I was working on and the next, I put it all together. Trig will be the end of me I will take you up on that offer without being a pest hopefully. Self teaching myself A2 maths is troublesome. I do love the student room though
Well I'm resisting this summer so its kinda helpful to be asked to work stuff out
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