Reciprocal and inverse trigonometric functions and compound angle identities (HL)

Learning objectives

Define the reciprocal ratios sec θ, cosec θ and cot θ, sketch their graphs and use the identities 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ

Sketch the graphs of arcsin x, arccos x and arctan x, state their domains and ranges, and use them to find exact values and solve equations

Use the compound angle identities for sin(A ± B), cos(A ± B) and tan(A ± B) and the double angle identity for tan to expand, simplify and find exact values

Prove trigonometric identities and solve equations by combining compound angle, double angle, Pythagorean and reciprocal identities

Use the symmetry and periodicity of the trigonometric graphs to relate the values of the functions at related angles, such as sin(π − x), cos(−x) and tan(x + π)