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c2 trig identities

Hi
Find the x-coordinates of the points where the curve y = 2 sin x intersects the curve y = 2 − 3cos2 x, for values of x such that −180º ≤ x ≤ 180º.

so i know that 2sinx=2=2-3cos^2 x
so far ive done:

2(1-cosx)=2-3cos^2 x
2-2cosx=2-3cos^2 x
3cos^2 x-2cosx = 0
cosx(3cosx-2)=0

cosx=2/3 and cosx=0?

But checked the mark scheme and they've gone the other way where they made everything into sinx. I know how to do this way but why do they not allow cosx?How do I know which one to change it into?
was that
2sinx=2-3cos^2x ?
You need to use the identity:
cos^2 x + sin^2 x =1
so cos^2 x=1-sin^2 x
so that
2-3(1-sin^2 x) -2sinx=0
2 -3 + 3sin^2x -2sinx=0
3sin^2x -2sinx -1=0
then put into a quadratic and solve to find sinx=whatever.
Sorry if i made any little mistakes in double negatives or whatever:smile:
Reply 2
Avatar for DonBorat
DonBorat
1
Original post by sach21sk
Hi
Find the x-coordinates of the points where the curve y = 2 sin x intersects the curve y = 2 − 3cos2 x, for values of x such that −180º ≤ x ≤ 180º.

so i know that 2sinx=2=2-3cos^2 x
so far ive done:

2(1-cosx)=2-3cos^2 x
2-2cosx=2-3cos^2 x
3cos^2 x-2cosx = 0
cosx(3cosx-2)=0

cosx=2/3 and cosx=0?

But checked the mark scheme and they've gone the other way where they made everything into sinx. I know how to do this way but why do they not allow cosx?How do I know which one to change it into?


sinx doesnt equal 1-cosx.

it is easier if your make sinx the subject
Sorry, that didnt answer the question!
Because you have cos^2x in the equation, not sin^2x ,you cannot use the trig identity for sin^2x so have to turn the cos^2x into sin.
Reply 4
Avatar for sach21sk
sach21sk
OP
Original post by DonBorat
sinx doesnt equal 1-cosx.

it is easier if your make sinx the subject


Original post by geology.is.gneiss
Sorry, that didnt answer the question!
Because you have cos^2x in the equation, not sin^2x ,you cannot use the trig identity for sin^2x so have to turn the cos^2x into sin.


does the rule cosx + sinx = 1 not work? or is that not even an identity, i thought it was
(edited 11 years ago)
Reply 5
Avatar for TenOfThem
TenOfThem
18
Original post by sach21sk
does the rule cosx + sinx = 1 not work?


No


Because it is not true
Reply 6
Avatar for steve2005
steve2005
17
Original post by sach21sk
does the rule cosx + sinx = 1 not work?


What rule is this ?
Original post by steve2005
What rule is this ?

nonexistant im afraid:/
the sin and cos have to be squared...
OP: at least you know now, and dont mess up in the exam!
Reply 8
Avatar for sach21sk
sach21sk
OP
Original post by steve2005
What rule is this ?


nvm, i thought cos^2 x + sin^2 x = 1 had the same rule to that but it doesn't

Original post by geology.is.gneiss
nonexistant im afraid:/
the sin and cos have to be squared...
OP: at least you know now, and dont mess up in the exam!


lol yeah so glad I found out before tomorrow, thanks :tongue:
(edited 11 years ago)
Original post by sach21sk
nvm, i thought cos^2 x + sin^2 x = 1 had the same rule to that but it doesn't



lol yeah so glad I found out before tomorrow, thanks :tongue:


Your exams tomorrow? Not edexcel then I guess?
And remember the other one, sinx/cosx=tanx does not involve ^2 signs:biggrin:

GOOD LUCK!!!! :biggrin: :biggrin: :biggrin:
Reply 10
Avatar for sach21sk
sach21sk
OP
Original post by geology.is.gneiss
Your exams tomorrow? Not edexcel then I guess?
And remember the other one, sinx/cosx=tanx does not involve ^2 signs:biggrin:

GOOD LUCK!!!! :biggrin: :biggrin: :biggrin:


No ocr :tongue: yep!

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