Name: Radian Measure (3.1.2) | IB DP Maths: AI HL Revision Notes 2021 Membership
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3.1.2 Radian Measure

Radian Measure

What are radians?

Radians are an alternative to degrees for measuring angles
1 radian is the angle in a sector of radius 1 and arc length 1
- A circle with radius 1 is called a unit circle
Radians are normally quoted in terms of π
- 2π radians = 360°
- π radians = 180°
The symbol for radians is ^c but it is more usual to see rad
- Often, when π is involved, no symbol is given as it is obvious it is in radians
- Whilst it is okay to omit the symbol for radians, you should never omit the symbol for degrees
In the exam you should use radians unless otherwise indicated

5-4-1-radian-measure-notes-diagram-1

How do I convert between radians and degrees?

Use π ^c= 180° to convert between radians and degrees
- To convert from radians to degrees multiply by $\frac{180}{π}$
- To convert from degrees to radians multiply by $\frac{π}{180}$
Some of the common conversions are:
- $2 π^{c} = 360 °$
- $π^{c} = 180 °$
- ${\frac{π}{2}}^{c} = 90 °$
- ${\frac{π}{3}}^{c} = 60 °$
- ${\frac{π}{4}}^{c} = 45 °$
- ${\frac{π}{6}}^{c} = 30 °$
It is a good idea to remember some of these and use them to work out other conversions
Your GDC will be able to work with both radians and degrees

5-4-1-radian-measure-notes-diagram-2

Worked Example

Convert 43.8° to radians.

aa-sl-3-1-2-radian-measure-we-solution-part-i

ii) Convert

\frac{5 π}{4}

to degrees.

aa-sl-3-1-2-radian-measure-we-solution-part-ii

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IB DP Maths: AI HL

Revision Notes

3.1.2 Radian Measure

Radian Measure

What are radians?

How do I convert between radians and degrees?

Worked Example

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