13.2A General Angles
Alg. II
Angles In Standard
Position
Recall: Angle- formed by two rays that
have a common endpoint, called the
vertex.
Generated by…
1. Fixing one ray (the initial side)
2. Rotating the other ray (the
terminal side) about the vertex
Standard position-In a coordinate plane, an angle
whose vertex is at the origin and whose
initial side is the positive x-axis.
Angles in Standard
Position
• Measure of an angle
– Determined by amount and direction of
rotation from the initial side to the
terminal side.
– Positive if the rotation is
counterclockwise
– Negative if the rotation is clockwise.
(terminal side of an angle can
make more than one full rotation)
Angles in Standard Position
Terminal
side
y
90°
0°
x
180°
vertex
Initial side
270°
360°
Drawing Angles in Standard
Position
Example 1Draw an angle with the given measure in
standard position. Then tell in which quadrant the terminal
side lies.
a. -120 °
b. 400 °
Quadrant II
Quadrant I
-120 °
Quadrant IV
Quadrant III
Quadrant I
400 °
Finding Coterminal
Angles
• Two angles in standard position are
coterminal if their terminal sides
coincide (or match up).
• Can be found by adding or
subtracting multiples of 360 ° to the
angle.
Finding Coterminal
Angles
Example 2 – Find one positive and one negative angle that are
coterminal with (a) -100 ° and (b) 575 °
a.
Positive coterminal angle: -100 ° + 360 ° = 260 °
Negative coterminal angle: -100 ° - 360 ° = -460 °
b.
Positive coterminal angle: 575 ° - 360 ° = 215 °
Negative coterminal angle: 575 ° - 720 ° = -145 °
Finding Coterminal
Angles
• Angles can also be measured in radians.
Radians- the measure of an angle in standard position whose
terminal side intercepts an arc length r.
Circumference of circle = 2 π(r), meaning there are 2 π radians in a
full circle.
Also meaning (360 ° = 2 π radians) and (180 ° = π radians)
13.2B Conversions Between
Degrees and Radians
• Degree Measure in Radians
– To rewrite, multiply by
π radians
180°
• Radian Measure in Degrees
– To rewrite, multiply by
180°
π radians
.
Converting Between
Degrees and Radians
Example 3
a. Convert 320 ° to radians.
16 π radians
9
b. Convert - 5 π
12
radians
to degrees.
-75 °
Arc Lengths & Areas of
Sectors
• Sector – a region of a circle that is
bounded by two radii and an arc of
the circle.
• Central angle  of a sector – the
angle formed by two radii.
Arc length s  r
1 2
A r 
2
Ex. 4 Find the arc length
and area of sector
• With radius of 5 centimeters and a

central angle of 45
Ex. 5 Evaluate the trig
function using a calc.
• (Or tables on pg. 861 & 853) for

sin
6