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