Odd

THE SIX TRIG FUNCTIONS

COSECANT FUNCTION f(x)=csc(x)


- Domain: All real numbers except kπ
- Range: (-∞,-1]U[1,∞)
- y-intercept: y=1
- Symmetry: Symmetric with respect to the origin
- Vertical asymptotes: x=kπ
- Period: 2π

SECANT FUNCTION f(x)=sec(x)


- Domain: All real numbers except π/2+kπ
- Range: (-∞,-1]U[1,∞)
- y-intercept: y=1
- Symmetry: Symmetric with respect to the y axis
- Vertical asymptotes: x=π/2+kπ
- Period: 2π

COTANGENT FUNCTION f(x)=cot(x)


- Domain: All real numbers except kπ
- Range: All real numbers
- x-intercepts: x=π/2+kπ
- Symmetry: Symmetric with respect to the origin
- Vertical asymptotes: x=kπ
- Period: π

SINE FUNCTION f(x)=sin(x)


- Domain: All real numbers
- Range: [-1,1]
- x-intercepts: x=kπ, k is an integer.
- y-intercept: y=0
- Maximum points: (π/2 + 2kπ,1)
- Minimum points: (3π/2 + 2kπ, -1)
- Symmetry: Symmetric with - respect to the origin.
- Period:2π

COSINE FUNCTION f(x)=cos(x)


- Domain: All real numbers
- Range: [-1,1]
- x-intercepts: x=π/2, k is an integer.
- y-intercept: y=1
- Maximum points: ( 2kπ , 1)
- Minimum points: ( π + 2kπ , -1)
- Symmetry: Symmetric with - respect to the y-axis
- Period:2π

TANGENT FUNCTION f(x)=tan(x)


- Domain: All real numbers except π/2 + kπ
- Range: All real numbers
- x-intercepts: x=kπ
- y-intercept: y=0
- Symmetry: Symmetric with - respect to the origin
- Vertical asymptotes: x=π/2 + kπ
- Period: π

FUNDAMENTAL TRIG IDENTITIES

1/sinθ = cscθ

1/cosθ = secθ

sin(-θ)=-sinθ

cos(-θ)=cosθ

tan(-θ)=-tanθ

1/tanθ = cotθ

tanθ = sinθ/cosθ

sin^2θ+cos^2θ=1

tan^2θ+1=sec^2θ

1+cot^2θ=csc^2θ