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Grade 11 Math Lab: Transcendence & Limits FREE

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Secant, Cosecant & Cotangent

60 min Grade 11 Math Lab: Transcendence & Limits

Learning Objectives

  • Define reciprocal trig functions
  • Graph sec, csc, cot
  • Apply identities

Key Concepts

Secant

sec(θ) = 1/cos(θ)

Cosecant

csc(θ) = 1/sin(θ)

Cotangent

cot(θ) = cos(θ)/sin(θ) = 1/tan(θ)

Theory

**Reciprocal Functions:** - sec(θ) = 1/cos(θ) — undefined when cos = 0 - csc(θ) = 1/sin(θ) — undefined when sin = 0 - cot(θ) = cos(θ)/sin(θ) — undefined when sin = 0 **Graphs:** Have vertical asymptotes where the base function = 0. **Identity:** 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ

Examples

Find sec(60°)

Solution: sec(60°) = 1/cos(60°) = 1/(½) = 2