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

What is the value of x?

(2 s.f. in degree)

Fill in the Blanks

What is the value of y?

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:

Fill in the Blanks

Change these angles to degrees.

$\frac{4}{9}\pi$

Fill in the Blanks

Change these angles to degrees.

$\frac{4}{15}\pi$

Fill in the Blanks

Change these angles to degrees.

$\frac{5}{12}\pi$

​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