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Mathematics LibreTexts

4: Basic Trigonometry

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”The whole universe is based on rhythms. Everything happens in circles. . . ” - John Hartford

The functions we have worked with so far have all been created by adding, subtracting, multiplying, and dividing power functions. While these cover a wide array of different curves, there are other more specific tools that we can use when dealing with circles and triangles. Chapter four is dedicated to two circular functions with big implications.

We begin with the Pythagorean Theorem for right triangles and use it to define the distance formula in the Cartesian plane. The distance formula immediately leads us to the equation for the graph of a circle in addition to its circumference and area formulas.

We define the sine and cosine functions in terms of the unit circle, and discuss their domains and graphs, as well as some easy to evaluate points for each, and how they interact with limits.

Trigonometry is the art of using these two functions to solve problems inside of triangles. We can define four additional trigonometric functions in terms of sine and cosine, (named secant, cosecant, tangent and cotangent) and their domains and graphs as well. Lastly we look into some basic identities to relate these trigonometric functions to one another in different ways.

Click through the following links to read this chapter.


This page titled 4: Basic Trigonometry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Ken Huber.

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