BallinteerInstitute?1995-2004
www.leavingcertsolutions.com
AniceproofforCos(A-B)usingvectors.
ThisproofusestheScalarproducttofindanexpressionforCos(A-B).
Weusethefactthatifarevectorsthat
→→
ba,
(1)θCosbaba=
→→
.(2)andifbdacbajdicbjbiaa+=?+=+=
→→→→→→→
.,
→
i
→
j
→→
+=jSinBiCosBq)(
B
A-B
→→
+=jAiCosApsin)(
TheProofgoesasfollows
circlethismeansthat
→→
1==
→
→
q
p.Justwriteoutt
.1.1)(.CosBACosqpqp=?=
→→
SinASinBCosACosBqp+=
→→
.?
ToFindCos(A+B)justreplaceBby–B.
andp
heScalarProduc
)(BA=?
ACos?(
aretwovectorsasshownontheunitq
tofpandqtwice.
)(BACos?
SinASinBCosACosBB+=)
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