7.4 Pythagorean Identities€¦ · 7.4 Pythagorean Identities Start with a circle: x2 + y2 = r2...
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PreCalculus 12 1 7.4 Pythagorean Identities Start with a circle: x 2 +y 2 =r 2 divide by r 2 to get Using sin cos y x and r r θ θ = = , this now becomes: Instead of dividing by r 2 , we can also divide by x 2 or y 2 to get two more Pythagorean identities: We will usually see these in the form of ____________________: i.e. 2 2 sin cos 1 θ θ + = à
Transcript of 7.4 Pythagorean Identities€¦ · 7.4 Pythagorean Identities Start with a circle: x2 + y2 = r2...
PreCalculus 12
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7.4PythagoreanIdentities
Startwithacircle: x2+y2=r2 dividebyr2toget
Usingsin cosy xandr r
θ θ= = ,thisnowbecomes:
Insteadofdividingbyr2,wecanalsodividebyx2ory2togettwomorePythagoreanidentities:
Wewillusuallyseetheseintheformof____________________:
i.e. 2 2sin cos 1θ θ+ = à
PreCalculus 12
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Example: prove: sinӨcosӨtanӨ=1-cos2Ө
OnyourOwn:prove csc # cos% # + sin # = csc #
PreCalculus 12
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WhenProvingaTrigIdentity:
1. Pickthemorecomplicatedsideandtrytoreduceittothesimplerside(thisisusuallyeasier)2. Lookatwhereyouneedtogetto(i.e.lookatthesideyouwillnotbechanging)
Ø Lookforpatterns:i. DoIneedtoeliminateorcancelafraction?ii. Arethereanyconjugates?àprobablyhavetomultiplybytheconjugatetoeliminateit
3. Createaplantogetthere(doyouforseetheuseofanidentity?Trytostay1stepahead)4. Ifindoubt,trysomething.Thesolutioncouldbemoreobviousafterwards.
Example: prove: 21 1 2sec1 sin 1 sin
θθ θ+ =
+ −
PreCalculus 12
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OnyourOwn: prove: sin cossin cos
csc secθ θ
θ θθ θ+
=+
Example Usealgebratosolvetheequation2 cos% , − 3 sin , = 0overthedomain0% ≤ , ≤ 22
Assignment:P.626#3(a,c,e),4,5,8,9,10MC1/2
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