4 Circular Motion

4 Circular Measure

​Arranged by : FIWA's Math Teacher

Poll

Ready to Learn?

• YES

• NO

Open Ended

What is your motivation in learning Math?

Poll

Which of the following terms that you know the meaning of.

• Degree

• Radian

• Arc Length

• Sector Area

• Chord

Learning Objectives

In this section you will learn how to:

» understand the definition of a radian.
» use the relationship between radians and degrees.
» use the formulae s = r.θ and A = 1/2 . r²θ in solving problems concerning the arc length and sector area of a circle.

Math Response

Find the perimeter of a sector of a circle with radius 6 cm and sector angle 30° .

Type answer here

Correct Answer: 12+\pi

Deg^°

Rad

Math Response

Find the area of a sector of a circle with radius 6 cm and sector angle 30° .

Type answer here

Correct Answer: 3\pi

Deg^°

Rad

Fill in the Blanks

Fill in the Blanks

Radians

the circumference (an arc of length 2πr) subtends an angle of 2π radians at the center, therefore:







When an angle is written in terms of π, we usually omit the word radian (or rad).

Hence, π = 180° .

Radians

Converting from degrees to radians

Worked Example:

Change 30° to radians, giving your answer in terms of π.

Math Response

Convert these degrees into radians

150°.

(Answer in term of π)

Type answer here

Correct Answer: \frac{5}{6}\pi

Deg^°

Rad

Math Response

Convert these degrees into radians

225°.

(Answer in term of π)

Type answer here

Correct Answer: \frac{5}{4}\pi

Deg^°

Rad

Math Response

Convert these degrees into radians

450°.

(Answer in term of π)

Type answer here

Correct Answer: \frac{5}{2}\pi

Deg^°

Rad

Converting from radians to degrees

Worked Example:

​Remember!

We can quickly find other angles, such as 120°, using these known angles.

​Checklist of Learning

Replace this with your body text.

​Duplicate this text as many times as you would like.

​

Try the exercise 4A