Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20130630 13:18:06
Sine InverseProvided 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' 'Who are you to judge everything?' Alokananda #2 20130630 14:21:23
Re: Sine InverseDraw right triangles ABC and PQR. 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. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20130630 14:46:44
Re: Sine InverseSin 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} (20130630 14:49:10) There are 10 kinds of people in the world,people who understand binary and people who don't. #4 20130630 21:54:07
Re: Sine InverseThanks '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' 'Who are you to judge everything?' Alokananda #5 20130807 01:02:06
Re: Sine Inverse
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' 'Who are you to judge everything?' Alokananda #7 20130807 02:56:16
Re: Sine InverseWhat 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' 'Who are you to judge everything?' Alokananda #9 20130807 09:02:47
Re: Sine Inverse
Start with two right angled triangles, both with hypotenuse c. Let one have angle A and the other B. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20130808 01:36:04
Re: Sine InverseIn that case are we not assuming that A + B = 90degree ?
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' 'Who are you to judge everything?' Alokananda #11 20130808 01:56:01
Re: Sine InverseI thought that you would have found post #2 particularly relevant. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20130808 18:21:39
Re: Sine Inversehi Agnishom, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei 