Trig graphs

The sine and cosine graphs are waves that repeat every 360°, going between −1 and 1. The tangent graph repeats every 180° and has asymptotes where cos is zero.

Key facts

  • y = sin x starts at 0, peaks at (90°, 1).
  • y = cos x starts at (0°, 1).
  • Both have period 360° and amplitude 1.
  • y = tan x has period 180° and asymptotes at 90°, 270°…
  • y = a sin bx: amplitude a, period 360°/b.

Worked examples

Example 1

What are the amplitude and period of y = 3 sin 2x?

  1. The 3 stretches it vertically: amplitude 3.
  2. The 2 squashes it horizontally: period 360 ÷ 2 = 180°.

Answer: Amplitude 3, period 180°

Example 2

Use the graph of y = cos x to solve cos x = 0.5 for 0° ≤ x ≤ 360°.

  1. cos 60° = 0.5.
  2. The cos graph is symmetric about 180°, so the other solution is 360 − 60 = 300°.

Answer: 60° and 300°