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#1 2013-06-29 15:18:06

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
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Sine Inverse

Provided that A and B are acute angles and sin A = sin B, prove that A = B


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
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#2 2013-06-29 16:21:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 96,586

Re: Sine Inverse

Draw right triangles ABC and PQR.

Prove that B = Q

We know that Sin B = Sin Q so:

We can manipulate the above to

b / q = c / r = k

b = kq and c = kr

Pull the k^2 out to simplify.

So

ΔABC is similar to ΔPQR

B = Q

View Image: 2013-06-29_211802.gif

In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#3 2013-06-29 16:46:44

{7/3}
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Registered: 2013-02-11
Posts: 210

Re: Sine Inverse

Sin A=a/c and sin B=b/c then a=b ,so in two right triangles with angle A and B ,oposite side is a=b,hypottenuse is c,other side must be equal.thus two triangles are congruent,A=B

Last edited by {7/3} (2013-06-29 16:49:10)


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#4 2013-06-29 23:54:07

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,744
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Re: Sine Inverse

Thanks smile


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#5 2013-08-06 03:02:06

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,744
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Re: Sine Inverse

{7/3} wrote:

Sin A=a/c and sin B=b/c then a=b ,so in two right triangles with angle A and B ,oposite side is a=b,hypottenuse is c,other side must be equal.thus two triangles are congruent,A=B

But the two right triangles are not congruent! You certainly cannot say that two right triangles containing equal angles are congruent.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#6 2013-08-06 04:43:11

bob bundy
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Registered: 2010-06-20
Posts: 7,055

Re: Sine Inverse

They both have a side 'c'.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2013-08-06 04:56:16

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,744
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Re: Sine Inverse

What if they do not have?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#8 2013-08-06 05:25:35

zetafunc.
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Re: Sine Inverse

Are you required to give a geometric proof?

#9 2013-08-06 11:02:47

bob bundy
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Registered: 2010-06-20
Posts: 7,055

Re: Sine Inverse

Agnishom wrote:

What if they do not have?

Start with two right angled triangles, both with hypotenuse c.  Let one have angle A and the other B.

Use the equal sines property to show that a = b.  Then they are congruent.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2013-08-07 03:36:04

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,744
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Re: Sine Inverse

In that case are we not assuming that A + B = 90degree ?

zetafunc wrote:

Are you required to give a geometric proof?

Well, yeah. But I would love to see any other proofs you have


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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#11 2013-08-07 03:56:01

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 96,586

Re: Sine Inverse

I thought that you would have found post #2 particularly relevant.


In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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#12 2013-08-07 20:21:39

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,055

Re: Sine Inverse

hi Agnishom,

Let's start again, shall we.  Draw a right angled triangle with angle A, hypotenuse c, opposite a.  Draw another with hypotenuse c and opposite B.  See diagram below.

From the first sinA = a/c

from the second sinB = b/c

But sinA = sinB , therefore a/c = b/c , therefore a = b

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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