Transcript Angles and Polar Coordinates

Angles and Polar Coordinates
Angles
• Angles are a way to describe the
difference in slope of two intersecting
lines
Vertex
Angle
Angles
• We measure the area in between the
lines, and compare it to a full circle
• We divide the circle into 360 equal parts
• See how many of those parts will fit in
between the two lines
Angles
• Typical angles go from 0 to 360 degrees
• The abbreviation for “degree” is a small
circle next to the number
37 degrees = 37°
Right Angle
• Any two intersecting lines that makes a
perfectly square corner
• Measures exactly 90°
• Another word for two lines at right angles
is “perpendicular”
Acute Angle
• A “sharp” angle
• Measures less than 90°
Obtuse Angle
• An angle larger than a right angle, less
than a straight line
• Between 90° and 180°
Measuring Angles
1. Place the center hole of the protractor over the vertex
or point of the angle
2. Align the zero line on the straight edge of the
protractor with one of the sides of the angle
3. Find the point where the second side of the angle
intersects the curved edge of the protractor and
read the number
Cartesian Coordinates
• Two axes, usually named X and Y
• At right angles to each other
Y axis
X axis
Origin
(0,0)
Cartesian Coordinates
• Plot how far things are from the origin
along the X and the Y axes (X,Y)
The red dot is 2
away from the
origin in the Y
direction
Y
3
(3,2)
2
1
1
X=3
Y=2
2
3
4
X
The red dot is 3 away
from the origin in the X
direction
Polar Coordinates
• Used to measure things around a circle
• Plot things in terms of an angle and a
distance to the origin
angle = 90°
Origin
angle = 180°
angle = 270°
angle = 0°
Polar Coordinates
angle = 90°
(distance, angle)
angle = 180°
angle = 0°
angle = 270°
Polar Graph Paper
Circles on the inside
represent different
distances
If this line
represents all the
possible points
with distance = 4
The numbers
around the outside
tell you the angles
Then the point
(4, 100°) is here
Review
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Angles are circular measurements
Right angles are 90° angles
Acute angles are less than 90°
Obtuse angles are more than 90°
Polar coordinates measure the angle from
a given line, and distance from the origin
• They are written as (distance, angle)