Trigonometry

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

Basic Concepts

The Unit Circle and Angle Measurement

Measuring Angles: Degrees and Radians

Angles can be measured in degrees (°) or radians. There are 360° in a circle, but only \(2\pi\) radians.

  • Degrees: Commonly used in daily life.
  • Radians: The language of mathematics and science.

\[ 360^\circ = 2\pi \text{ radians} \] \[ 1 \text{ radian} = \frac{180^\circ}{\pi} \]

The Unit Circle

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. Each point on the circle corresponds to an angle, and its coordinates \((x, y)\) are \((\cos \theta, \sin \theta)\).

Why is the Unit Circle Important?

It helps us understand trigonometric functions for all angles, not just those in right triangles.

Examples

  • Converting 90° to radians: \(90^\circ = \frac{\pi}{2}\) radians.

  • On the unit circle, the coordinates at 180° are (-1, 0).

In a Nutshell

The unit circle links angles, radians, and trigonometric functions in a visual way.

The Unit Circle and Angle Measurement - Trigonometry Content | Practice Hub