Trignometry

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.

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

Types of Coordinate Systems Cartesian Plane polar

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

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,  )

Trigonometry Review

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

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

Example - Answer Home 6 blks 13 blks

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 

Example - Answer #1 Home 6 blks 13 blks  blks

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

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

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°

Example - Answer Flagpole Distance = 40 m 31°