Graphs of sin, cos and tan

What this chapter teaches

A point going round a circle of radius 1 has height sin x and distance across cos x. Their graphs are waves between −1 and 1 that repeat every 360°. The tan graph has asymptotes at 90° and 270°. An equation like sin x = 0.5 has two solutions between 0° and 360°, found with the calculator and then by symmetry.

Three questions to ask

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

1. Where does the sin wave start, and what are its highest and lowest values?
2. How do you find the second angle when sin x = 0.5, after the calculator gives 30°?
3. Why does the tan graph have gaps at 90° and 270°?

After the chapter, the learner can

• Sketch y = sin x and y = cos x up to 360°
• Use a graph to find two angles with sin x = 0.5