### Memory aid for Compound Angles

PostPosted:

**Tue Nov 18, 2003 3:06 am**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!

/\

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!