This document discusses circular measure and calculating various values related to circles. It defines the radian unit and explains how to convert between radians and degrees. It provides formulas for calculating arc length, radius, angles subtended, perimeter of circle segments, and area of sectors and segments. Examples are given for converting between radians and degrees and calculating arc lengths, areas of sectors and segments.

1. Circular measure
Chapter 8

2. OBJECTIVE
• Understand the concept of radian
• Determine
a) Length of arc
b) Radius
c) Angle subtended at the center of a circle
based on given information
d) Find perimeter of segment of circle
e) Area of sector and segment

3. Concept Map
Circular measures
Arc length,s
s= rѲ
Π rad = 180⁰
x 180⁰/ π
X π/180⁰
degree radian
Area of segment AB
= Sector of AOB –
Area of ∆ OAB
= ½ r²Ѳ - ½ r² sinѲ
= ½ r²(Ѳ - sinѲ)
Area of sector A
A= ½ r² Ѳ

4. Convert measurements in radian to
degrees and vice versa
• Convert angle in degrees to radian ( in term of π)
a. 30⁰ =
b. 270 ⁰ =
• Convert angle in radian to degrees ( in term of
degree and minute)
a. ⅗ π rad=
b. 0.215 rad=

5. Calculate length of arc(s)
a) b)

6. Find the area of sector( shaded area)
a)
b)

7. Find the area of segment (shaded area)
1.64 rad
1,98 rad
a) b)