Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Basic Concepts

The Unit Circle and Radian Measure

Making Sense of the Unit Circle

The unit circle is a circle with a radius of 1, centered at the origin of a graph. It helps us understand how sine and cosine work for all angles, not just those in triangles!

Radians Explained

Instead of degrees, angles can be measured in radians. One full circle is \(2\pi\) radians, which equals \(360^{\circ}\). So,

  • \(180^{\circ} = \pi\) radians
  • \(90^{\circ} = \frac{\pi}{2}\) radians

Connecting to Trigonometry

Every point on the unit circle has coordinates (\(\cos(\theta), \sin(\theta)\)). This means you can find the sine and cosine of any angle using the unit circle.

Examples

  • On the unit circle, the point at 90° (\(\frac{\pi}{2}\) radians) is (0, 1).

  • At 180° (\(\pi\) radians), the point is (-1, 0).

In a Nutshell

The unit circle lets us find sine and cosine for any angle using radians.