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

Agnishom
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From: The Complex Plane
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.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
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#2 2013-06-29 16:21:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
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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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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)


There are 10 kinds of people in the world,people who understand binary and people who don't.

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
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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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

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

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
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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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

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

bob bundy
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Registered: 2010-06-20
Posts: 6,531

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: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
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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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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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: 6,531

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: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
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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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Online

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,531

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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