# Introduction to Trigonometry

## 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

In a right triangle, sec θ = 4. Sketch the triangle, place the ratio numbers, and evaluate the remaining functions of θ.

To say that sec θ = 4, is to say that the hypotenuse is to the adjacent side in the ratio 4 : 1.

$$4 = \frac{4}{1}$$ To find the unknown side x, we use Pythagoras formula. $$a^2 + b^2 = c^2$$ $$x^2 + 1^2 = 4^2$$ $$x^2 + 1 = 16$$ $$x^2 = 16 - 1$$ $$x^2 = 15$$ $$x = \sqrt{15}$$

## You'll use it...

To calculate unknown values.

## Video

### Basic Trigonometry

Watch a Khan Academy Video »
Length: 9:17

## Video

### The Six Trig Ratios

Watch a Khan Academy Video »
Length: 4:45

## Video

### Using Trig to Solve for Missing Information

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Length: 6:12

## Video

### Radian and Degree Conversion Practice

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Length: 7:12