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

step 1 We want to use the unit circle to evaluate the cosine of negative 90 degrees. Normally, we would

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

Key Concepts

Trigonometric Function Values

Determining exact trigonometric function values involves understanding the relationships and symmetries presented by the unit circle along with the even-odd properties of the functions. Using these concepts, one can find the values of sine and cosine for standard angles, including the simplification of expressions involving negative angles.

Odd Function

An odd function satisfies the condition f(-x) = –f(x) for every x in its domain. In trigonometry, the sine function is odd, which implies that sin(–?) = –sin(?). This symmetry property helps in determining the sine values for negative angles by relating them to their positive counterparts.

Even Function

An even function is one that satisfies the equation f(-x) = f(x) for every x in its domain. In the context of trigonometry, the cosine function is even, meaning that cos(–?) = cos(?) for any angle ?. This property allows for the simplification of computations involving negative angles.

Unit Circle

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It serves as a fundamental reference tool in trigonometry, allowing the definition of sine and cosine functions based on the coordinates of a point corresponding to a given angle. This visualization makes it easier to understand and calculate trigonometric values for various angles.

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