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# C3 - Trig question watch

1. Hi,

could someone please give me a detailed description and working out for this question as I dont seem to understand how you do them....Iv got the basics of expanding the formulas etc but im really quite confused...!!

(i)Express 4 cosθ − sinθ in the form Rcos(θ + α ), where R > 0 and 0◦ < α < 90◦. [3]

(ii) Hence solve the equation 4 cosθ − sinθ = 2, giving all solutions for which −180◦ < θ < 180◦.
[5]

WILL REP THE MOST CONCISE ANSWER!!!
thank you
2. ok

i) R is the square root of 4 squared + 2 squared
To find the angle you do cos/sin as in 4/1 then do inverse tan of this answer

ii) you use the previuos answer to work out the angles
3. First expand the RHS:
4cosx-sinx=Rcosxcosa - Rsinxsina

[Mod edit: Please don't post full solutions. Read the posting guide sticky at the top of the thread list.]

(ii)use your Rcos(x+a) formula from (i) and solve!
4. I didn't help which is a good reason to rep me.
5. (Original post by SK-mar)
Hi,

could someone please give me a detailed description and working out for this question as I dont seem to understand how you do them....Iv got the basics of expanding the formulas etc but im really quite confused...!!

(i)Express 4 cosθ − sinθ in the form Rcos(θ + α ), where R > 0 and 0◦ < α < 90◦. [3]

(ii) Hence solve the equation 4 cosθ − sinθ = 2, giving all solutions for which −180◦ < θ < 180◦.
[5]

WILL REP THE MOST CONCISE ANSWER!!!
thank you
i) Use the cos(A+B) rule and expand. Remember to write 'R' in front. A = θ and B = α

Next step. You must group the terms together where you will find Rcosα and Rcosθ and that will be equal to a number.

You know that Rcosα = x and Rcosθ = y (whatever number you get, in this case 4 & 1).

Then, you draw a right angled triangle, fill in the lengths, O and A and work out R by using pythag. Work out what tana = O/A and do inverse tan to find out what a is. Now you have R and a. Re-write.

ii) From part i, you have formed an equation in the form of Rcos(θ + α ) = 2 (2's given in question)

Divide by the value of R by bringing it across to the RHS, so you get: 2/R

Solve like normal trig.

Hope it helps.
6. (Original post by *MJ*)
It works so why do I care.

You guys go back and do sina / cosa to obtain tana and then do tan^-1 right?

I find it's easier, just stick the R back in and obtain the angle.

yeah. But, it's funner to make it tan! Honest.
I don't like dealing with R, since it's usually a surd, and I hate surds!
7. (Original post by SK-mar)
sweet thanks......just wandering tho, strictly speaking, in case i get another type, should it be Rsina = -1? as its 4cosa - Sina.....

and could u actually do part ii.) for me so I fully understand, i will then rep you!!! thankssss
it's not -1 because it's also -Rsinxsina on the RHS. If that made any sense.
8. (Original post by *MJ*)
It works so why do I care.

You guys go back and do sina / cosa to obtain tana and then do tan^-1 right?

I find it's easier, just stick the R back in and obtain the angle.

I draw a right angled triangle. Label cos and sin, work out R using pythag. Then work out tana by O/A.
9. (Original post by unamed)
yeah. But, it's funner to make it tan! Honest.
I don't like dealing with R, since it's usually a surd, and I hate surds!
True mathematicians love surds.

I even eat them for breakfast.
10. (Original post by *MJ*)
True mathematicians love surds.

I even eat them for breakfast.
I'm not a true mathematician, then. I'm a physicist - and we like our calculus.
We do it in our sleep.

[by the way, i swear you were a girl the other day! ]
11. (Original post by *MJ*)
True mathematicians love surds.

I even eat them for breakfast.
right that was verrrrry heplful I completely get it now thankyou so much.....not just you but everyone who posted....Im gonna rep MJ but wish I could rep you all, sorry to those who I havnt!! but thanks anyway!!! ......... btw in these question will it most likely always be in the form
show that xcosa - xsina = Rcos(x-a) ....basicaly do they only use COS and SINE in C3, on the left hand side??
12. (Original post by SK-mar)
right that was verrrrry heplful I completely get it now thankyou so much.....not just you but everyone who posted....Im gonna rep MJ but wish I could rep you all, sorry to those who I havnt!! but thanks anyway!!! ......... btw in these question will it most likely always be in the form
show that xcosa - xsina = Rcos(x-a) ....basicaly do they only use COS and SINE in C3 on the left hand side??
Thanks and yes.

You may get 2sinx + 5cosx for example.

Solving 2secx = 3 is a totally different question.

13. Just a reminder people, posting full solutions here is not permitted. Please see the posting guide at the top of the thread list.
14. (Original post by gottastudy)
I draw a right angled triangle. Label cos and sin, work out R using pythag. Then work out tana by O/A.
That is one long method, it is just an excuse for you to draw triangles??
15. (Original post by Illusionary)
Just a reminder people, posting full solutions here is not permitted. Please see the posting guide at the top of the thread list.
I actually never knew this! I shall obey the rule from now on.
16. (Original post by crazedmonkey09)
That is one long method, it is just an excuse for you to draw triangles??
Yes. I have finally mastered drawing perfect right angled triangles.

Spoiler:
Show
Actually, I just learnt the method in the book.

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