Trigonometric functions, graphs and equations

Learning objectives

Sketch the graphs of sin x, cos x and tan x, stating their amplitude (where defined), period, domain, range and asymptotes

Sketch and interpret functions of the form f(x) = a sin(b(x + c)) + d and the corresponding cosine and tangent forms, relating each parameter to a transformation of the basic graph

Model periodic phenomena such as tides, temperatures and Ferris wheels with sinusoidal functions, determining the parameters from a description, a table or a graph

Solve trigonometric equations in a given finite interval analytically, using the unit circle or the symmetry of the graph to find all solutions, and graphically using technology

Solve trigonometric equations that require identities, including equations that reduce to a quadratic in sin x, cos x or tan x