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A level maths trignometry help

How do I convert sin^2 x/2 into 1-cosx/2 ?
Reply 1
Avatar for mqb2766
mqb2766
21
Original post by keeno25
How do I convert sin^2 x/2 into 1-cosx/2 ?

Half or double angle formula.

Edit - brackets really would help. I originally thought is was a mistyped Pythagorean identity (the bear). Still not 100% sure
(edited 3 years ago)
sin2Θ ≡ 1 - cos2Θ

so just let Θ = x/2
Reply 3
Avatar for keeno25
keeno25
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17
Original post by the bear
sin2Θ ≡ 1 - cos2Θ

so just let Θ = x/2

They say the answer is (1-cox)/2
Reply 4
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keeno25
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Original post by keeno25
They say the answer is (1-cox)/2


Original post by the bear
sin2Θ ≡ 1 - cos2Θ

so just let Θ = x/2

I dont understand how
Reply 5
Avatar for mqb2766
mqb2766
21
Original post by keeno25
I dont understand how

Have you looked at the half angle identity (or double angle identity)?
Are you trying to derive it?
Reply 6
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keeno25
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Original post by mqb2766
Have you looked at the half angle identity (or double angle identity)?
Are you trying to derive it?

I used the sin squared x plus cos squared x =1 formula. Is that the right one to use?
Reply 7
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mqb2766
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Original post by keeno25
I used the sin squared x plus cos squared x =1 formula. Is that the right one to use?

No. It's a standard identity (half of double angle), not the Pythagorean identity. I guess the bear got confused due to the lack of brackets in the OP.
Are you trying to prove it? What is the actual question?
(edited 3 years ago)
Reply 8
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keeno25
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17
Original post by mqb2766
No. It's a standard identity (half of double angle), not the Pythagorean identity. I guess the bear got confused due to the lack of brackets in the OP.
Are you trying to prove it? What is the actual question?

I am just confused as to how to rearrange it into that form as part of a question.
The answer steps say: (sin^2x)/2= 2sinx
(1-cosx)/2= 2sinx
Reply 9
Avatar for mqb2766
mqb2766
21
Original post by keeno25
I am just confused as to how to rearrange it into that form as part of a question.
The answer steps say: (sin^2x)/2= 2sinx
(1-cosx)/2= 2sinx

Can you upload an image? You've changed the equation again.
Reply 10
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keeno25
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17
Original post by mqb2766
Can you upload an image? You've changed the equation again.

Here it is
Capture 3.PNG7.1KB
Original post by keeno25
Here it is

The left hand side substitution in the first two lines is the half angle identity.
Have you looked it up in your formula sheet/googled it?
Reply 12
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keeno25
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Yh

Original post by mqb2766
The left hand side substitution in the first two lines is the half angle identity.
Have you looked it up in your formula sheet/googled it?

Yh its cos2x= 1-2sin^2x
But how would you rearrange that?
Original post by keeno25
Yh


Yh its cos2x= 1-2sin^2x
But how would you rearrange that?

To get
sin^2(x/2) = (1 - cos(x))/2
Have a go, it's a couple of simple steps. Just rearrange the equation.

You could just look at the half angle identity, but derive it from the double if you want.
Reply 14
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keeno25
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17
Original post by mqb2766
To get
sin^2(x/2) = (1 - cos(x))/2
Have a go, it's a couple of simple steps. Just rearrange the equation.

You could just look at the half angle identity, but derive it from the double if you want.

We haven't learn the half angle formulae yet.
I keep getting sin^2=-cos2x+1
I have no clue what to do from there
Original post by keeno25
We haven't learn the half angle formulae yet.
I keep getting sin^2=-cos2x+1
I have no clue what to do from there

You could still look at it (half angle identity).
Can you show your steps, and pls use brackets.
Reply 16
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keeno25
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17
Original post by mqb2766
You could still look at it (half angle identity).
Can you show your steps, and pls use brackets.

Ohhh I see how u do it now using the half angled formula. Thanks very much

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