Trigonometric functions, exact values and graphs

Learning objectives

Define sine, cosine, tangent, secant, cosecant and cotangent for angles of any magnitude, positive or negative, and use the quadrant rule to determine the sign of each

Recall the exact values of the trigonometric ratios for 0, π/6, π/4, π/3 and π/2 and their related angles, and use them to give exact answers without a calculator

Sketch the graphs of y = sin x, y = cos x and y = tan x over a stated interval, stating the amplitude and period of each and the positions of the asymptotes of the tangent graph

Sketch and interpret the graphs of y = a sin(bx) + c, y = a cos(bx) + c and y = a tan(bx) + c, describing the effect of a on amplitude, of b on period and of c on the vertical shift

Determine the number of solutions of an equation such as a sin(bx) + c = k within a given interval by comparing a sketch of the curve with the horizontal line y = k