Math104 Precalculus Angles and Radian Measure Notes 4.1

I. Definitions

• Angle:

• Types of angles:

acute:

right:

obtuse:

straight:

• Standard position:

quadrantal angle

Math104 Precalculus Notes 4.1 page 2 of 3

II. Angle Measures

• Degrees:

• Radians:

• Examples:

1. Convert the following degree measures to radians:

(a) 30º (b) 135º (c) -780º

2. Convert the following radian measures to degrees

(a)

(b)

3. Convert 2.5 revolutions counter-clockwise to degree measure.

• Coterminal angle:

ex #1: -135º ex #2: -110º ex #3: 300º

Math104 Precalculus Notes 4.1 page 3 of 3

III. Arc Measure

• Examples:

1. Find the length of the arc subtended by a central angle of 60º in a circle of radius 12 m.

2. Find the measure of the central angle, θ subtending the arc s of length 2 meters on the unit

circle. Use 3.14 to obtain an approximation to the degree measure of the angle. Round your

answer to the nearest tenth of a degree.