In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -𝜋 40

Key Concepts

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find a coterminal angle, you can add or subtract multiples of 2π (or 360 degrees) from the given angle. For example, if you have an angle of -π, adding 2π results in a positive coterminal angle.

Radians and Degrees

Angles can be measured in radians or degrees, with 2π radians equivalent to 360 degrees. Understanding the relationship between these two units is crucial for converting angles and finding coterminal angles. In this case, -π radians is equivalent to -180 degrees, which helps in visualizing the angle's position on the unit circle.

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is a fundamental tool in trigonometry for understanding angles and their corresponding sine, cosine, and tangent values. By visualizing angles on the unit circle, one can easily determine coterminal angles and their properties.