Module 4: Lesson 4.01 - Angles and Their Measurements

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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?


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