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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
sin
cos
tan
opposite side
hypotenuse
adjacent side
hypotenuse
opposite side
adjacent side
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
2 2 2r x y
1sin 0.707 45
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
a2 b2 c 2
62 132 c 2
c 2 36 169
c 2 205
c 205
c 14.32 blocks from home
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
14.32 blks
sin() opposite
hypotenuse
sin 1 opposite
hypotenuse
sin 1 13
14.32
65.2
Example - Answer #2
Home
6 blks
13 blks
14.3 blks
cos() adjacent
hypotenuse
cos 1 adjacent
hypotenuse
cos 1 6
14.32
65.2
Example - Answer #3
Home
6 blks
13 blks
14.3 blks
tan() opposite
adjacent
tan 1 opposite
adjacent
tan 1 13
6
65.2
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°
tan() opposite side
adjacent side
tan(31 ) flagpole height
40 metersFlagpole Height 40 meters tan(31 )
Flagpole height 24 meters tall