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Unit 3 Trigonometry Project (Trigonometric Functions (tanx=y/x, cscx=r/y,…

- - - - cos(a-B)=cosacosB-sinasinB
    - - cos(a+B)=cosacosB-sinasinB
    - - sin(a+B)=sinacosB+cosasinB
    - - tan(a-B)=(tana-tanB)/(1+tanatanB)
    - - sin(a-B)=sinacosB-cosasinB
    - - tan(a+B)=(tana+tanB)/(1-tanatanB)
- - - - tanx=sinx/cosx
      - cotx=cosx/sinx
    - - 1+tan^2x=sec^2x
      - 1+cot^2x=csc^2x
      - sin^2x+cos^2x=1
    - - tanx=1/cotx
      - sinx=1/cscx
      - cscx=1/sinx
      - cosx=1/secx
      - secx=1/cosx
      - cotx=1/tanx
    - - cos(-x)=cos
      - sec(-x)=secx
      - csc(-x)=-cscx
      - tan(-x)=-tanx
      - sin(-x)=-sinx
      - cot(-x)=-cotx

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Unit 3 Trigonometry Project

Unit 3 Trigonometry Project

Sum and Difference Formulas

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Difference for Cosine

Sum for Cosine

Sum for Sine

Difference for Tangent

Difference for Sine

Sum of Tangent

sin(a-B)=sinacosB-cosasinB

sin(a+B)=sinacosB+cosasinB

cos(a-B)=cosacosB-sinasinB

cos(a+B)=cosacosB-sinasinB

tan(a-B)=(tana-tanB)/(1+tanatanB)

tan(a+B)=(tana+tanB)/(1-tanatanB)

Trigonometric Functions

tanx=y/x

cscx=r/y

cosx=x/r

secx=r/x

sinx=y/r

cotx=x/y

Double-Angle & Half-Angle Formulas

Double-Angle Formulas

Half-Angle Formulas

an2x= (2tanx)/(1-tan^2x)

cos2x=cos^2x-sin^2x

sin2x=2sinxcosx

cos2x=2cos^2x-1

cos(a/2)= +-√ (1+cosa)/2)

tan(a/2)= +-√ (1-cosa)/1+cosa)

sin(a/2)= +-√ (1-cosa)/2)

tan(a/2)=(1-cosa)/(sina)

tan(a/2)= (sina)/(1+cosa)

Verifying Trig Identities

Fundamental Identities

Quotient Identities

Pythagorean Identities

Reciprocal Identities

Even-Odd Identities

tanx=1/cotx

sinx=1/cscx

cscx=1/sinx

cosx=1/secx

secx=1/cosx

cotx=1/tanx

tanx=sinx/cosx

cotx=cosx/sinx

1+tan^2x=sec^2x

1+cot^2x=csc^2x

sin^2x+cos^2x=1

cos(-x)=cos

sec(-x)=secx

csc(-x)=-cscx

tan(-x)=-tanx

sin(-x)=-sinx

cot(-x)=-cotx