Precalculus
Lesson 2 of 3 9 min +60 XP

Intro to Trigonometry

Sine and cosine as waves.

What you'll learn

  • Relate sine to the unit circle
  • Recognize the sine wave
  • Read amplitude and period
The Ferris wheel seat

Ride a Ferris wheel and your height rises, peaks, falls, and repeats in a smooth wave. Plot that height against time and you've drawn a sine curve — trigonometry describes anything that cycles round and round.

Going around the circle

On the unit circle, the sine of an angle is the height (y-coordinate) and cosine is the horizontal position (x-coordinate). As the angle increases, the height traces out the smooth, repeating sine wave.

Simulation · Wave: amplitude & frequency

This is the shape of sine: change the frequency to change the period, and the amplitude to change its height.

Lab · Sine at key angles
  1. At 0°, the height on the unit circle is 0 — so sin(0) = 0.
  2. At 90°, the point is at the top — so sin(90°) = 1.
  3. Picture the wave rising from 0 up to 1.

What you should see: sin(0°) = 0 and sin(90°) = 1 — the wave rises from zero to its peak of 1.

Knowledge Check

+15 XP / correct

1. On the unit circle, sine corresponds to which coordinate?

2. What is sin(90°)?