Transcript Trigonometry for Physics

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
opposite side
sin  
hypotenuse
adjacent side
cos  
hypotenuse
opposite side
tan  
adjacent side
More Trigonometry

Pythagorean Theorem
r  x y
2

2
To find an angle, you need the inverse trig
1
function
  sin 0.707  45
–

2
for example,
Be sure your calculator is set appropriately
for degrees or radians
Example

13 blks
You walk 6 blocks
east and then 13
blocks north. As the
crow flies, how far are
you from home?
6 blks
Home
Example - Answer
a2  b2  c 2
13 blks
6 2  132  c 2
c 2  36  169
c 2  205
c  205
c  14.32 blocks from home
Home
6 blks
Example

13 blks
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
Example - Answer #1
13 blks
opposite
sin( ) 
hypotenuse
 opposite 
1
  sin 

hypotenuse
1 13 
  sin 

14.32
  65.2
14.32 blks

Home
6 blks
Example - Answer #2
13 blks
adjacent
cos( ) 
hypotenuse
 adjacent 
1
  cos 

hypotenuse

1 6
  cos 

14.32
  65.2
14.3 blks

Home
6 blks
Example - Answer #3
13 blks
opposite
tan( ) 
adjacent


1 opposite
  tan 

adjacent
113
  tan  
 6 
  65.2
14.3 blks

Home
6 blks
Example

Flagpole
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?
31°
Distance = 40 m
opposite side
adjacent side
flagpole height
tan(31) 
40 meters
Flagpole Height 40 meterstan(31)
tan( ) 
Flagpole

Example - Answer
Flagpole height 24 meters tall
31°
Distance = 40 m