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By midoh
#3533
As an alternative to consulting a Mathematical Table to solve Sin(A+B), Sin(A-B), Cos(A+B),Cos(A-B) & other combinations I suggest the following scheme:

             /\
           s/  \c   This is 'Mt.Sin A,B
          o/    \o  To get Sin(A+B),start
         c/same \s on the left slope,you
         / sign   \ get,sin(a).cos(b)+(same
        /----|-----\ sign),cos(a).sin(b)
      n/     |      \s likewise,Sin(A-B),
     i/  (-) |  (+)  \i again start on the
    s/ R.H.S.| L.H.S. \n left slope,you get,
    /___*2___|____*2___\ sin(a).cos(b)-(same sign)cos(a).sin(b)

Sin(A+B)+Sin(A-B) is got by covering the left-hand side of the mountain and multiplying by 2. So you get 2*sinAcosB, likewise Sin(A+B)-Sin(A-B) is got by covering the r.h.s. of the mountain so you get 2*CosA.SinB.'Mt.Cos A,B is slightly different. The left slope is COS,COS & the right slope is SIN,SIN. Also at the apex is the admonition invert sign, the rest of the scheme is the same. So Cos(A+B)=?,left slope,COS,COS>cosA.cosB,apex-invert sign,(A+B)>cosAcosB-sinAsinB, and so on.

Reward: positive feedback from struggling maths students on whether this helps!
User avatar
By Steve
#3556
Once more, this time with a better font:
Code: Select all             /\
           s/  \c   This is 'Mt.Sin A,B
          o/    \o  To get Sin(A+B),start
         c/same  \s on the left slope,you
         / sign   \ get,sin(a).cos(b)+(same
        /----|-----\ sign),cos(a).sin(b)
      n/     |      \s likewise,Sin(A-B),
     i/  (-) |  (+)  \i again start on the
    s/ R.H.S.| L.H.S. \n left slope,you get,
    /___*2___|____*2___\ sin(a).cos(b)-(same sign)cos(a).sin(b)
By midoh
#3646
:-#

I hate it when graphics don't turn out the way you want!
so here goes another attempt to get it right.


******************** /\
******************* /....\
****************** /........\
******************/........... \
***************** / ............. \
**************** / same sign . \
*************** /-------------------\
************** / ......................... \
going up**************************** coming down right
left slope! *************************** slope!
^ ************************************ \/
sin, cos *********************************** cos, sin
*******************************************************
(SIN(A+B)= sina.cosb...+(same sign)..cosa.sinb)
(SIN(A-B)= sina.cosb...-(same sign)..cosa.sinb)
to subtract these 2 compound angles cover the right slope and
multiply the left slope by 2,gives...2cosasinb to add two compund
angles do the reverse ,cover RHS ..so LHS*2=2sina cosb
User avatar
By Steve
#3647
Midoh, if my attempt doesn't look the way you wanted, maybe you can just send me a screenshot of what it looks like on your machine? I'll be more than happy to post it! :-)
By Rishi
#4472
Thanks, Midoh!
Brings me back memories of Loney's Trigonometry. I love Nemonics. This combination of both is nice. Reminds me of the steep emrald hill sides dotted with sheep.on the coastal drive we took from Galway last October. Ireland is a lovely country.

I am sure every math student will appreciate your 'sin'ful hills 'cos they reduce the tedium.

Rishi
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