# Second Semester Geometry

### Survival Guide

## Chapter 8: Trigonometry

Key Ideas

- Pythagorean Theorum
- SOH-CAH-TOA Trigonomic Device
- Inverse ""
- Degree and Radian Measures
- Special Right Triangles
- Unit Circle

## Pythagorean Theorum

A squared + B squared = C squared (base squared + height squared = hypothenuse [longest side])

- Only works on right triangles

## Trigonometric Ratios

- The sides and the angles of triangles and the trigonometric functions are related.
- SOH CAH TOA
- Shows what the missing side measure is

## What SOH CAH TOA stands forThe opposite/adjacent/hypotenuse refers to what side it is in comparison to the angle measurement given. | ## Where the Sides AreAngle A is the given angle measurement in this case. | ## Example ProblemThe missing side was cut off at the bottom. |

## Inverse Trigonometric Functions

- Shows what the missing side measure is
- Sets it up like the picture shown

## Angle of Elevation/Depression

- Deals with viewpoint of people/things
- Used to find out how high or at what angle things are at

## Angle of ElevationCalculate by using SOH CAH TOA | ## Angle of Depressioncongruent to the angle of elevation | ## BOTH COMBINED IN THE SAME PICTUREMIND BLOWN |

## 6 Trig Functions

Pretty straight forward. The formulas are in the picture. They are sine, cosine, tangent, cosecant, secant, and cotangent.

## Degree and Radian Measures

You can measure with both degrees and radians. In a unit circle, there are degrees and radians. The degree is obviously the angle measure of each angle, and the radian measure is what it is in terms of Pi.

- To rewrite a degree measure in radians, multiply be Pi radians over 180 degrees, and the reciprocal of that for radians to degree measure.
- You use the unit circle in these problems.

## Special Right Triangles

Theorem: In a 30-60-90 triangle the sides are in the ratio 1:2:the square root of 3

## Tips!

- Use a calculator it makes your life much easier
- Don't overthink the problem
- Write out ALL your work

## Things We Struggled With

- The Unit Circle and Radians. That was just hard to understand.
- Angle of Depression was hard at first, but with practice it got easier.