Unit 4 Day 4
Precalculus
Notes
Name:
Date:
Degrees, Radians, Complementary and Supplementary Angles
Standard position : that the initial side of the angle is on the
x-axis.
A quadrantal angle: an angle whose terminal side is on an axis (either the x-axis or the y-axis.)
Positive Angles
Negative Angles
Rotate Counterclockwise
Rotate Clockwise
II
Degree
Radian
One full
revolution around
circle of radius, r
360°
One full
revolution around
circle of radius, r
2π
One radian is the
measure of the
radius of the
circle.
III
I
IV
Converting between degrees and radians
Radians to Degrees
Degrees to Radians
π
180°
)
(multiply by
)
(multiply by
180°
π
Convert the following radians to degrees:
Convert the following degrees to radians:
5π
270°
When you want to "get rid of" π place π in the denominator:
When you want to "get rid of" degrees place the degree
measure 180º in the denominator:
270° •
1)
π
180°
5π •
=
Convert to 75° to radians
2) Convert
180°
π
=
9π
to degrees
4
3) Convert 3 to degrees
Coterminal angles: angles that have the same
and
side.
To find: add or subtract revolutions (360° or 2π) depending on the given form.
Two typical instructions options are:
Find a positive and a negative coterminal angle.
Find a coterminal angle between 0° and 360° or between 0 and 2π.
Coterminal Angles
Find a positive and a negative coterminal angle for each:
Example 1
Example 3
Example 2
400°
−
Adding
340°
−
2π
3
Adding
400º +360º = 760º
−
11π
+
2π •3
−
11π
+
6π
= −
−
5π
+
6π
=
Subtracting
400º - 360º = 40º
(Not Negative)
Subtract another
40º - 360º = -220º
11π
3
Example 4
3
3
3
1 •3
3
3
5π
3
π
3
Find a coterminal angle in [0°, 360°] or [0, 2π]. (ONE possible answer)
Example 5
400°
Not between
Adding
400º +360º = 760º
−
9π
4
−
9π
+
2π •4
−
9π
+
8π
−
4
4
π
4
+
8π
between
4
= −
=
37π
6
−
Not
1 •4
4
Example 8
–210°
Adding
Subtracting
400º - 360º = 40º
Example 7
Example 6
π
4
7π
4
Complementary angles are two positive angles whose sum is
or
.
or
.
(Only acute angles
have complements)
Supplementary angles are two positive angles whose sum is
#1 – 2: If possible, find the compliment.
1) 23°
2)
4π
5
#3 – 4: If possible, find the supplement.
3) 23°
4)
4π
5
*Complements and Supplements are never negative.*