Reciprocal Function: Secant
r/x
Range: (-∞, -1]U[1, ∞)
Domain: x != π/2 + πn
Period: 2π
Even: f(x) = f(-x)
x/r
Range: [-1, 1]
Domain: all real numbers
Period: 2π
Even: f(x) = f(-x)
Neither even nor odd
Domain: [-1, 1]
Range: [0, π]
Cofunction Identities
sin θ = cos(π/2 - θ)
cos θ = sin(π/2 - θ)
sec θ = csc(π/2 - θ)
csc θ = sec(π/2 - θ)
tan θ = cot(π/2 - θ)
cot θ = tan(π/2 - θ)
Pythagorean Identities
sin² θ + cos² θ = 1
1 + tan² θ = sec² θ
1 + cot² θ = csc² θ
Even Odd Identities
sin(-θ) = -sin θ
tan(-θ) = -tan θ
cos(-θ) = cos θ
Reciprocal Identities
sin θ = 1/csc θ
cos θ = 1/sec θ
tan θ = 1/cot θ
Quotient Identities
tan θ = sin θ/cos θ
cot θ = cos θ/sin θ
Reciprocal Function: Cosecant
r/y
Range: (-∞, -1]U[1, ∞)
Domain: x != πn
Period: 2π
Odd: -f(x) = f(-x)
y/r
Range: [-1, 1]
Domain: all real numbers
Period: 2π
Odd: -f(x) = f(-x)
Odd: -f(x) = f(-x)
Domain: [-1, 1]
Range: [-π/2, π/2]
Reciprocal Function: Cotangent
x/y
Range: all real numbers
Domain: x != πn
Period: π
Odd: -f(x) = f(-x)
y/x
Range: all real numbers
Domain: x != π/2 + πn
Period: π
Odd: -f(x) = f(-x)
Odd: -f(x) = f(-x)
Domain: all real numbers
Range: [-π/2, π/2]