Download 5.1: Angles and Radian Measure Angles If an angle is in standard

5.1 Homework:
One assignment on Math XL
5.1: Angles and Radian Measure
Angles
If an angle is in standard position:
-its vertex lies at the origin.
-its initial side lies along the positive x-axis.
Degrees
Remember how angles had to be between 0 and 180 in
geometry? Well, buckle up folks, because that’s not the case
anymore! For example:
225°
270°
810°
-390°
Radians
Here is one way to define the unit of a radian:
Suppose we have a circle with a radius of 1 unit.
 The circumference of this circle is _______. Now take any
central angle in this circle.
 If the measure of that central angle is 𝜃°, then the length of
the arc subtended by that angle is the also the measure of
the angle in radians. Let’s take a couple examples:
Here is another way to define a radian:
Cool gif:
https://en.wikipedia.org/wiki/Radian#/media/File:Circle_radians.
gif
1.
Convert from degree measure to radian measure:
a.
60°
b.
117°
c.
−447°
2.
Convert from radian measure to degree measure:
a.
b.
𝜋
2
𝜋
6
5𝜋
c.
−
d.
1 radian
3
3.
Draw and label each angle in standard position
𝜋
a.
𝜃=−
b.
𝛼=
3𝜋
c.
𝛾=
13𝜋
6
4
4
A chart that may or may not be useful:
Two angles in standard position are coterminal iff they have the
same terminal side.
4.
Find angles that are coterminal to the following angles.
a. 450°
b.
c.
d.
1110°
15𝜋
4
−
𝜋
12
Arc Length
5.
Solve.
a. A circle has a radius of 24 meters. Find the length of the arc
intercepted by a central angle of 150°.
b.
When Mr. Cawelti rode the Carousel of
Happiness in Nederland, he did 1.5
revolutions before he got sick and they
had to close the ride. If the distance from
the center of rotation to his horsie was 20
feet, how far did he travel?