The Six Trigonometric Functions, Their Inverses, and the Fundamental Trigonometric Identities.
Csc(X) Function
f(x) = csc (x)
Properties
Domain: all real numbers except k pi, k is an integer.
Range: (-infinity , -1] U [1 , +infinity)
Period = 2pi
Vertical asymptotes: x = k pi, where k is an integer.
f(x) = arccsc (x)
Properties
Domain: (−∞,−1]∪[1,∞)
Range: [−π/2,0)∪(0,π/2]
Asymtote: y= -pi
Sec(X) Function
f(x) = sec (x)
Properties
Domain: all real numbers except pi/2 + k pi, n is an integer
Range: (-infinity , -1] U [1 , +infinity)
Period = 2 pi
Vertical asymptotes: x = pi/2 + k pi, where k is an integer.
f(x) = arcsec (x)
Properties
Domain: (−∞,−1]∪[1,∞)
Range: [0,π/2)∪(π/2,π]
Asymptote: y = -pi
Cot(X) Function
f(x) = cot (x)
Properties
Domain: all real numbers except k pi, k is an integer
Range: all real numbers
Vertical asymptotes: x = k pi, where k is an integer.
Period = pi
f(x) = arccot (x)
Properties
Domain: (−∞,∞)
Range: (0,π)
Astmtote: y=pi/4; 17pi/4
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)
Pythagorean Identities
Sin^2(x) + Cos^2(x) = 1
1 + Tan^2(x) = Sec^2(X)
1 + Cot^2(X) = CSC(x)
Sin(X) Function
f(x) = sin (x)
Properties
Domain: all real numbers
Range: [-1 , 1]
Period = 2pi
f(x) = arcsin (x)
Properties
Domain: [−1,1]
Range: [−π/2,π/2]
Cos(X) Function
f(x) = cos (x)
Properties
Domain: all real numbers
Range: [-1 , 1]
Period = 2pi
f(x) = arccos (x)
Properties
Domain: [−1,1]
Range: [0,π]
Tan(X) Function
f(x) = tan (x)
Properties
Domain: all real numbers except pi/2 + k pi, k is an integer.
Range: all real numbers
Period = pi
f(x) = arctan (x)
Properties
Domain: (−∞,∞)
Range: (−π/2,π/2)
Quotient identities
TAN (X) = Sin(X)/Cos(X)
COT (X) = Cos(X)/Sin(X)