Use the unit circle and the fact that sine is an odd function and cosine is an even function to

step 1 I want to use the unit circle to evaluate the cosine of negative 135 degrees. If we think about

Use the unit circle and the fact that sine is an odd...

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Key Concepts

Even and Odd Functions

In trigonometry, functions can be classified as even or odd based on their symmetry properties. An even function, like cosine, satisfies the condition cos(??) = cos(?), meaning its graph is symmetric with respect to the y-axis. An odd function, like sine, satisfies sin(??) = ?sin(?), which indicates symmetry about the origin. These properties simplify the evaluation of trigonometric functions at negative angles.

Exact Trigonometric Values

Exact trigonometric values refer to the precise values of trigonometric functions at standard angles, typically derived from the unit circle. These values are important for solving trigonometric problems without approximations and are frequently used in various branches of mathematics and physics. They provide a basis for understanding and computing the functions for specific angles.

Unit Circle

The unit circle is a fundamental tool in trigonometry defined as a circle with a radius of one centered at the origin of the coordinate plane. It is used to determine the sine and cosine values of angles by associating each angle with a point on the circle, where the x-coordinate represents the cosine value and the y-coordinate represents the sine value. This concept aids in visualizing and calculating trigonometric function values for any angle.

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