c2 trig identities
Maths and statistics discussion, revision, exam and homework help.
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c2 trig identitiesHi
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? -
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Re: c2 trig identitieswas 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
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Re: c2 trig identitiessinx doesnt equal 1-cosx.(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?
it is easier if your make sinx the subject -
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Re: c2 trig identitiesdoes the rule cosx + sinx = 1 not work? or is that not even an identity, i thought it was(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.Last edited by sach21sk; 17-05-2012 at 18:11. -
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Re: c2 trig identitiesNo(Original post by sach21sk)
does the rule cosx + sinx = 1 not work?
Because it is not true -
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Re: c2 trig identitiesWhat rule is this ?(Original post by sach21sk)
does the rule cosx + sinx = 1 not work? -
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Re: c2 trig identitiesnonexistant im afraid:/(Original post by steve2005)
What rule is this ?
the sin and cos have to be squared...
OP: at least you know now, and dont mess up in the exam! -
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Re: c2 trig identitiesnvm, i thought cos^2 x + sin^2 x = 1 had the same rule to that but it doesn't(Original post by steve2005)
What rule is this ?
lol yeah so glad I found out before tomorrow, thanks(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!
Last edited by sach21sk; 17-05-2012 at 18:18. -
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Re: c2 trig identitiesYour exams tomorrow? Not edexcel then I guess?(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
And remember the other one, sinx/cosx=tanx does not involve ^2 signs
GOOD LUCK!!!!
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Re: c2 trig identitiesNo ocr(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
GOOD LUCK!!!!
yep!
