(A Level) Secant, cosecant and cotangent

Learning objectives

Define sec θ = 1/cos θ, cosec θ = 1/sin θ and cot θ = 1/tan θ, and sketch their graphs for angles of any size, showing asymptotes, periods and ranges

Use sec²θ ≡ 1 + tan²θ and cosec²θ ≡ 1 + cot²θ to prove identities and to simplify expressions

Solve equations such as 3 tan²θ − sec θ = 1 or cot θ + 2 tan θ = 3 by forming a quadratic in a single ratio, giving all roots in a stated interval in degrees or radians

Find exact values of sec, cosec and cot at angles such as π/6, 3π/4 and 300°