Trig graphs and their changes

What this chapter teaches

y = sin x and y = cos x are waves with period 2π and amplitude 1. In y = a sin(bx + c) + d, a changes the height, b squeezes the graph sideways to give period 2π/b, c slides it left by c/b, and d lifts it up. y = tan x has period π and asymptotes at the odd multiples of π/2.

Three questions to ask

There is no one right wording. Listen for the idea.

1. What does the 3 do in y = 3 sin x, and what does it do in y = sin 3x?
2. Why does y = tan x have no amplitude?
3. Which way does y = sin(x + 1) move the graph of y = sin x?

After the chapter, the learner can

• Sketch y = 2 sin 3x and give its period and amplitude
• Sketch y = tan x and mark its asymptotes