Module 4: Lesson 4.01 - Angles and Their Measurements
How many radians are around a circle?
2ℼ
How many seconds are in a full rotation?
3600
How many minutes are in a full rotation?
60
Since 360 degrees is 2ℼ radians, how many degrees is ℼ rad?
ℼ rad = 180 degrees
How many radians is 1/4 the length around a circle?
ℼ/2
What does a degree with a ' (min) indicate?
A decimal 132° 50' = -132 + 50/60 = -132.83
What does min ' indiciate?
A minute
How would you find coterminal angles, with angles in radians?
Add & subtract 2ℼ from the given angle-radian value
How would you determine the quadrant of an angle given the angle measurement if the angle is negative?
Add 2ℼ to find the pos value of the angle, then find quadrant
How would you determine the quadrant of an angle given the degree measurement if the degree is negative?
Add 360 to determine the positive measurement, then find quadrant
Obtuse Angles
Angles > 90 degrees; btwn ℼ / 2 & ℼ
Acute Angles
Angles less than 90 degrees; btwn 0 & ℼ/2
Rotating a ray CCW & CW produces what type of angles?
CCW: positive angles CW: negative angles
Conversion from Radians to Degrees
Multiply by 180 / ℼ
Conversion from Degrees to Radians
Multiply by ℼ / 180
On what axis are initial sides always drawn & why?
Pos x-axis so that angles are in standard position
If a circle has its center located at the vertex of an angle, what is the distance from the center to the circle?
Radius r
Circumference
The distance around a circle; 2ℼ
Initial Side
The starting position of the ray
Ray
a line starting at an endpoint & extending indefinitely
Coterminal Angles
angles produced when two angles have the same initial & terminal side
Angle
the amount of rotation between two rays
What are the two methods of measuring angles?
radian measure & degree measure
What is a radian defined by?
ratio of arc length to radius
Arc Length Formula
s = r𝚹 arc(s) = radius(r) angle in radians(𝚹)
Vertex
the endpoint around which sides are rotated
Radian
the measure of a central angle 𝚹 that intercepts an arc s equal in length to the radius r of the circle
Terminal Side
the position of the initial ray after rotation
How many radians is a rotation half-way around a circle?
ℼ