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Unit 10- Analytic Trigonometry (10.2- Sum and Difference Formulas…
Unit 10- Analytic Trigonometry
10.1-Verifying Trig Identities
Fundamental Identities
Quotient Identities
tan
x
=sin
x
/cos
x
cot
x
=cos
x
/sin
x
Pythagorean Identities
sin^2x+cos^2x=1
1+tan^2x=sec^2x
1+cot^2x=csc^2x
Reciprocal Identities
sin
x
=1/csc
x
cos
x
=1/sec
x
tan
x
=1/cot
x
csc
x
=1/sin
x
sec
x
=1/cos
x
cot
x
=1/tan
x
Even-Odd Identities
sin(-x)=-sinx
csc(-x)=-cscx
cos(-x)=cos
cot(-x)=-cotx
tan(-x)=-tanx
sec(-x)=secx
10.2- Sum and Difference Formulas
Difference for Cosine
cos(a-B)=cosacosB-sinasinB
Sum of Cosine
cos(a+B)=cosacosB-sinasinB
Sum for Sine
sin(a+B)=sinacosB+cosasinB
Difference for Sine
sin(a-B)=sinacosB-cosasinB
Difference for Tangent
tan(a-B)=(tana-tanB)/(1+tanatanB)
Sum of Tangent
tan(a+B)=(tana+tanB)/(1-tanatanB)
10.3-Double Angle & Half-Angle Formulas
Double-Angle Formulas
cos2x=cos^2x-sin^2x
cos2x=2cos^2x-1
tan2x= (2tanx)/(1-tan^2x)
sin2x=2sinxcosx
Half-Angle Formulas
tan(a/2)= +-√ (1-cosa)/1+cosa)
tan(a/2)=(1-cosa)/(sina)
cos(a/2)= +-√ (1+cosa)/2)
tan(a/2)= (sina)/(1+cosa)
sin(a/2)= +-√ (1-cosa)/2)
Trigonometric Functions
tanx=y/x
cscx=r/y
cosx=x/r
secx=r/x
sinx=y/r
cotx=x/y