# Graphing

## What does it mean?

### Definitions:

From The Math Page:

$$sin θ = \frac{opposite}{hypotenuse}$$ $$csc θ = \frac{hypotenuse}{opposite}$$ $$cos θ = \frac{adjacent}{hypotenuse}$$ $$sec θ = \frac{hypotenuse}{adjacent}$$ $$tan θ = \frac{opposite}{adjacent}$$ $$cot θ = \frac{adjacent}{opposite}$$

Pythagorean Identities

$$sin^2 θ + cos^2 θ = 1$$ $$1 + tan^2 θ = sec^2 θ$$ $$1 + cot^2 θ = csc^2 θ$$

## What does it look like?

A general example to help you recognize patterns and spot the information you're looking for

Show: $$sec^2 x + csc^2 x = sec^2 x csc^2 x$$ Solution: The problem means that we are to write the left-hand side, and then show, through substitutions and algebra, that we can transform it to look like the right hand side. We begin: $$sec^2 x + csc^2 x = \frac{1}{cos^2 x} + \frac{1}{sin^2 x}$$ $$sec^2 x + csc^2 x = \frac{sin^2 x + cos^2 x}{cos^2 x sin^2 X}$$ $$sec^2 x + csc^2 x = \frac{1}{cos^2 x sin^2 x}$$ $$sec^2 x + csc^2 x = \frac{1}{cos^2 x} * \frac{1}{sin^2 x}$$ $$sec^2 x + csc^2 x = sec^2 x csc^2 x$$

## You'll use it...

Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

## Video

### Graph, Domain, and Range of Sine Function

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Length: 9:22

## Video

### Amplitude and Period

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Length: 8:21

## Video

### Graphs of Trig Functions

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Length: 9:55

## Video

### Figure Out the Trig Function

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Length: 6:34

## Video

### Trigonometric Identities

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Length: 9:09