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## #1 2013-06-30 13:18:06

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #2 2013-06-30 14:21:23

bobbym

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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

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #3 2013-06-30 14:46:44

{7/3}
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### 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} (2013-06-30 14:49:10)

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

## #4 2013-06-30 21:54:07

Agnishom
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### Re: Sine Inverse

Thanks

'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'
'The whole person changes, why can't a habit?' -Alokananda

## #5 2013-08-07 01:02:06

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #6 2013-08-07 02:43:11

bob bundy
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### 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

## #7 2013-08-07 02:56:16

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #8 2013-08-07 03:25:35

zetafunc.
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### Re: Sine Inverse

Are you required to give a geometric proof?

## #9 2013-08-07 09:02:47

bob bundy
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### 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

## #10 2013-08-08 01:36:04

Agnishom
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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'
'The whole person changes, why can't a habit?' -Alokananda

## #11 2013-08-08 01:56:01

bobbym

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### 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.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #12 2013-08-08 18:21:39

bob bundy
Moderator

Online

### 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