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10 cards from this deck
Cosecant is 1/sinθ1/\sin\theta1/sinθ, expressed as cscθ=1/sinθ\csc\theta = 1/\sin\thetacscθ=1/sinθ.
Undefined when sinθ=0\sin \theta = 0sinθ=0, at θ=nπ\theta = n\piθ=nπ, nnn integer.
Secant is 1/cos(θ)1/\cos(\theta)1/cos(θ), expressed as sec(θ)=1/cos(θ)\sec(\theta) = 1/\cos(\theta)sec(θ)=1/cos(θ).
Undefined when cosθ=0\cos \theta = 0cosθ=0, at θ=(2n+1)π/2\theta = (2n+1)\pi/2θ=(2n+1)π/2.
Cotangent is cosθ/sinθ\cos \theta/\sin \thetacosθ/sinθ, or cotθ=1/tanθ\cot \theta = 1/\tan \thetacotθ=1/tanθ.
Undefined when tanθ=0\tan \theta = 0tanθ=0, at θ=nπ\theta = n\piθ=nπ, nnn integer.
Range is (−∞,−1]∪[1,∞)(-\infty, -1] \cup [1, \infty)(−∞,−1]∪[1,∞).
The range of cotangent is all real numbers (−∞,∞)(-∞, ∞)(−∞,∞).
csc2θ=1+cot2θ\csc^2 \theta = 1 + \cot^2 \thetacsc2θ=1+cot2θ, derived from sin2θ+cos2θ=1\sin^2 \theta + \cos^2 \theta = 1sin2θ+cos2θ=1.
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