Section5.5–Multiple-AngleFormulas
Don’tworry,youdonothavetomemorizethefollowingformulas,butyouhavetoknowhowtouse
them….
Double-AngleFormulas
Ex.1)Usethefiguretofindtheexactvalueofthefollowing:
12
13
θ
sin2θ=
cos2θ=
tan2θ=
PrecalculusCP1
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Section5.5–Multiple-AngleFormulas
Ex.2)Findtheexactsolutionoftheequationintheinterval[0,2π)
sin2x
+
cosx = 0 !
Ex.3)Findtheexactsolutionoftheequationintheinterval[0,2π)
!cos2x + sinx = 0 Ex.4)Useadouble-angleformulatorewritetheexpression.
2
!6cos x − 3 π
Ex.5)Findtheexactvalueofthefollowingif!cscx = 3 ,and < x < π !2
!tan2x = PrecalculusCP1
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Section5.5–Multiple-AngleFormulas
θ
θ
θ
**Thesignsof sin and cos dependonthequadrantinwhich lies**
2
! 2
!
!2
Half-AngleFormulas
Ex.6)Usethefiguretofindtheexactvalueofthefollowing:
3
θ
4
θ
sin = ! 2
θ
tan = ! 2
u
5
π
Ex.7)Findtheexactvalueof tan if sinu =
and < u < π .
2 !
13
!
!2
PrecalculusCP1
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Section5.5–Multiple-AngleFormulas
Ex.8)Usethehalf-angleformulastodeterminetheexactvaluesof:
a) sin 22.5° !
b)!cos105° Ex.9)Usethehalf-angleformulastosimplifytheexpression.
1− cos8x
! sin8x
HW:5.5p.415:3,5,9,13,19,21,27,35,37,41,53,55
(
PrecalculusCP1
)
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