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

Place the center hole of the protractor over the vertex or point of the angle

Align the zero line on the straight edge of the protractor with one of the sides of the angle

Find the point where the second side of the angle intersects the curved edge of the protractor and read the number

1.

2.

3.

1.

2.

3.

Cartesian Coordinates

• Two axes, usually named X and Y

• At right angles to each other

X axis

Y axis

Origin(0,0)

Cartesian Coordinates

• Plot how far things are from the origin along the X and the Y axes (X,Y)

X

Y

1 2

3

4

2

1

3

The red dot is 3 away from the origin in the X

direction

The red dot is 2 away from the origin in the Y

direction

X = 3Y = 2

(3,2)

Polar Coordinates

• Used to measure things around a circle

• Plot things in terms of an angle and a distance to the origin

angle = 0°

angle = 90°

angle = 180°

angle = 270°

Origin

Polar Coordinates

(distance, angle)

angle

dist

ance

angle = 0°

angle = 90°

angle = 180°

angle = 270°

Polar Graph PaperThe numbers

around the outside tell you the angles

Circles on the inside represent different distances

If this line represents all the possible points with distance = 4

Then the point (4, 100°) is here

Review• 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)