1. Trignometry

2. What is TRIG?
Trigonometry is a branch of mathematics that developed from simple geometry, and surveying.
Trigonometry was probably invented for use in astronomy. The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago.

3. Coordinate Systems Used to describe the position of a point in space
Coordinate system consists of
a fixed reference point called the origin
specific axes with scales and labels
instructions on how to label a point relative to the origin and the axes

4. Types of Coordinate Systems
Cartesian
Plane polar

5. Cartesian coordinate system
Also called rectangular coordinate system
x- and y- axes
Points are labeled (x,y)

6. Plane polar coordinate system
Origin and reference line are noted
Point is distance r from the origin in the direction of angle , ccw from reference line
Points are labeled (r,)

7. Trigonometry Review

8. More Trigonometry Pythagorean Theorem
To find an angle, you need the inverse trig function
for example,
Be sure your calculator is set appropriately for degrees or radians

9. Example
You walk 6 blocks east and then 13 blocks north. As the crow flies, how far are you from home?
Home
6 blks
13 blks

10. Example - Answer
Home
6 blks
13 blks

11. Example
You walk 6 blocks east and then 13 blocks north. At what angle would you need to walk to go straight to your destination? (NOTE - several ways to solve…)
Home
6 blks
13 blks 

12. Example - Answer #1
Home
6 blks
13 blks
14.32 blks 

13. Example - Answer #2
Home
6 blks
13 blks
14.3 blks 

14. Example - Answer #3
Home
6 blks
13 blks
14.3 blks 

15. Example
A telescope pointed directly at the top of a distant flagpole makes an angle of 31° with the ground. If the scope is low to the ground and 40 m from the base of the pole, how tall is the pole?
Flagpole
Distance = 40 m
31°

16. Example - Answer
Flagpole
Distance = 40 m
31°