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

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bob bundy
2013-02-16 00:10:14

You're welcome.

Bob

One final thought:  The compound angle formulas work whatever the angles used.  They aren't limited to acute angles.  The proof above only works for acute angles; in fact, the diagram breaks down if A + B is over 90.  I think that is why I prefer other proofs that are more general.  The rotational matrix proof is my favourite.

{7/3}
2013-02-15 23:08:03

Yeah,thanks you helped me a lot in this post.

bob bundy
2013-02-15 22:00:26

hi

If you put alpha = beta = A, you get the double angle formulas.

eg.

Now put theta = 2A and you can re-arrange to get

and so on.

Is that what you wanted?

Bob

{7/3}
2013-02-15 21:33:24

Quick question:are these formulas used to find half angle formulas?

bob bundy
2013-02-15 19:03:15

hi {7/3}

Well done!

Bob

{7/3}
2013-02-15 12:03:29

Hi bob. I have derived the cosine's sum formula,and after trying a little i found the difference formulas too:),plus i know how to derive tangent's formula using sine and cosine

bob bundy
2013-02-15 04:00:58

OK.  Let me know how you get on.

Bob

{7/3}
2013-02-15 03:41:28

Thanks for your help,now i'm going to try to derive the cosine formula(thanks again).

bob bundy
2013-02-15 00:44:52

hi {7/3}

I did wonder if that's what you wanted.  I could remember the formulas I gave easily so I took the line of least effort.

There are many ways of proving the compound angle formulas.  The trig. approach is the first I met whilst still at school, but I haven't used it since.  So I've had to dig deep in my memory.

So, make a triangle ABC with angle A = alpha and angle B = 90

Make a perpendicular line CD so that angle DCA  = 90.

Choose the position of D so that DAC = beta.

Draw DF perpendicular to AB with F on AB, and finally CE perpendicular to DF with E on DF.

Call the point where DF and AC cross point G.

AGF = CGD = 90 minus alpha so GDC = alpha.

note EF = CB

The cosine formula is very similar.  I'll leave it as an exercise.

hint AF = AB - FB

Bob

{7/3}
2013-02-14 23:29:37

Sorry,I got confused with names of formulas(my mother-tongue isn't english )amd wrote wrong,I wanted to derive the compound angle formulas using trigonometry.

bobbym
2013-02-14 22:30:50

Hi;

I already did in the other thread. It looks like it is a tough nut to crack.

bob bundy
2013-02-14 22:23:45

Yes, me too.  All are acsii 43 so it's not that.

I'll post a note to MIF.

Bob

anonimnystefy
2013-02-14 22:19:12

Hmm... weird!

It's working for me, but only on its own!

bob bundy
2013-02-14 22:16:47

The + sign won't parse for me.

I've edited them to dotplus for now.

Bob

anonimnystefy
2013-02-14 22:15:28

Hi Bob

Why is "plus" written everywhere "+" should go.