Trigonometric functions, identities and equations

  • Six trigonometric functions for angles of any magnitude (in degrees or radians)

  • Principal values of sin–1x, cos–1x, tan–1x

  • Exact values of the trigonometric functions for special angles (30°, 45°, 60°) or ( π/6, π/4, π/3)

  • Amplitude, periodicity and symmetries related to sine and cosine functions

  • Graphs of y = a sin (bx) + c, y = a sin (x/b) + c, y = acos (bx) + c, y = a cos (x/b) + c and y = tan (bx) +c, where a is real, b is a positive integer and c is an integer.

  • Use of:

- sin A/ cos A = tan A, cos A/ sin A = cot A , sin2 A + cos2 A = 1, sec2 A = 1 + tan2 A, cosec2 A = 1 + cot2 A

- the expansions of sin(A ± B) , cos(A ± B) and tan(A ± B)

- the formulae for sin2A, cos2A and tan2A

- the expression of acosθ + bsinθ in the form Rcos(θ ±α ) or R sin(θ ±α)

  • Simplification of trigonometric expressions

  • Solution of simple trigonometric equations in a given interval (excluding general solution)

  • Proofs of simple trigonometric identities

  • Using trigonometric functions as models