The six trigonometric ratios are introduced by consideration of similar right triangles using angle measurement in both degrees and radians. The six general trigonometric functions are defined in terms of ratios formed from the x and y coordinates of ordered pairs in the Cartesian plane. Particular use is made of the ordered pairs one unit from the origin lying on the unit circle. The graphs of the basic 6 trigonometric functions are introduced and then variations in the amplitude, period and phase shift as well as the composition of functions are considered. The basic identities including the reciprocal, Pythagorean, addition, half and double angle identities are considered.
Emphasis is made both on evaluating trigonometric functions and proving various identities.
In addition, areas are found both by trigonometric methods and by Heron s formula. The polar form and rectangular form of complex numbers are introduced. The multiplication, division, powers and roots of complex numbers are developed using trigonometric form. The equations of the straight line, parabola, circle, ellipse and hyperbola are developed from their geometric properties. The reverse process is also considered to make explicit the important geometric properties given certain types of algebraic equation of certain types.