THE SIX TRIG FUNCTIONS

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FUNDAMENTAL TRIG IDENTITIES

1+cot^2θ=csc^2θ

tan^2θ+1=sec^2θ

sin^2θ+cos^2θ=1

tanθ = sinθ/cosθ

1/tanθ = cotθ

tan(-θ)=-tanθ

cos(-θ)=cosθ

sin(-θ)=-sinθ

1/cosθ = secθ

1/sinθ = cscθ

THE SIX TRIG FUNCTIONS

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

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

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

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

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

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