Trigonometrical Identities

Mr Pussyfoot

How can sin^2θ+cos^2θ ≡ 1 be rewritten in a form that involves only one Trigonometrical function? :s-smilie:

Reply 1

Mr T Pities You

Original post by Mr Pussyfoot

How can sin^2θ+cos^2θ ≡ 1 be rewritten in a form that involves only one Trigonometrical function? :s-smilie:

Could you use the relation between sine and cosine? You know the graphs look very similar, so how could you use this?
[I'm trying not to just give you the answer :smile:

]

Reply 2

studentwiz

sin2thetha = 2sinthetacostheta

sin^2 2theta =4sin^2theta cos^2theta

1-cos^2theta = sin^2theta

sub 4cos^2(1-cos^2) +cos^2theta=1

(edited 8 years ago)

Reply 3

Mr T Pities You

Original post by studentwiz

sin2thetha = 2sinthetacostheta

sin^2 2theta =4sin^2theta cos^2theta

1-cos^2theta = sin^2theta

sub 4cos^2(1-cos^2) +cos^2theta=1

Bear in mind that you may not have learnt these double angle formulae though.

Reply 4

Mr Pussyfoot

Original post by Mr T Pities You

Could you use the relation between sine and cosine? You know the graphs look very similar, so how could you use this?
[I'm trying not to just give you the answer :smile:

]

To be honest I'm a novice with identities, I know what each graph looks like (cosine is translated) but how would this help me??

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Reply 5

Mr T Pities You

Original post by Mr Pussyfoot

To be honest I'm a novice with identities, I know what each graph looks like (cosine is translated) but how would this help me??

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Okay, double check your notes as you should have somewhere that sin( pi/2 - theta) = cos theta
You can now just substitute that in to the identity above and it'll only have sines in it.
The method give by studentwiz above will be beyond your current level, so just ignore it (this year :wink:

)

Reply 6

Mr Pussyfoot

Original post by Mr T Pities You

)

I do GCSE Further Maths, I don't think it that you I've learned that at this stage. All I know are the identities and their rearranged forms.

The answer I'm supposed to get is 2sin^2theta - sin theta -1=0

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Reply 7

Mr T Pities You

Original post by Mr Pussyfoot

I'm not sure that is right. The original thing is an identity and is true for any value of theta. The equation you have given is only true for certain values of theta like 90 or 210 degrees.
Can you double check or let me know where the question came from.
I don't teach GCSE further maths, but I'd guess the trig identities you know are limited to first year a level.

Reply 8

Mr Pussyfoot

Original post by Mr T Pities You

ImageUploadedByStudent Room1432646240.295928.jpg

It's from a further maths workbook

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Reply 9

Mr T Pities You

Original post by Mr Pussyfoot

It's from a further maths workbook

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Now it makes sense! You've read the question incorrectly. It wants you to use the identity to rewrite each of the equations. I've started the first one for you - I hope it helps

Reply 10

Mr Pussyfoot

Original post by Mr T Pities You

Now it makes sense! You've read the question incorrectly. It wants you to use the identity to rewrite each of the equations. I've started the first one for you - I hope it helps