Degree and Radian Measures
What is Degree and Radian Measures?
A unit of angle measurement, where a full circle is divided into 360 equal parts.
Key formula / rule: Degree to Radian Conversion
Key points
- Understand the concept of angle measurement in degrees and radians.
- Learn the relationship between degrees and radians.
- Be able to convert angles from degrees to radians and vice versa.
- Apply these concepts to solve geometry and trigonometry problems.
Common exam trap
Confusing the conversion factors (using 180/π instead of π/180 and vice-versa).
Definitions
- Term
Degree
- Meaning
A unit of angle measurement, where a full circle is divided into 360 equal parts.
- Term
Radian
- Meaning
A unit of angle measurement defined by the radius of a circle; an angle subtended by an arc equal to the radius at the center of the circle.
- Term
Full Circle
- Meaning
A complete rotation, equivalent to 360 degrees or 2π radians.
Learning objectives
Understand the concept of angle measurement in degrees and radians.
Learn the relationship between degrees and radians.
Be able to convert angles from degrees to radians and vice versa.
Apply these concepts to solve geometry and trigonometry problems.
Formulae
- Name
Degree to Radian Conversion
- Note
Use this formula to convert an angle measured in degrees to its equivalent in radians.
- Expression
Radians = Degrees × (π/180)
- Name
Radian to Degree Conversion
- Note
Use this formula to convert an angle measured in radians to its equivalent in degrees.
- Expression
Degrees = Radians × (180/π)
Prerequisites
Basic understanding of angles (acute, obtuse, right, straight).
Familiarity with circles and their properties.
Basic arithmetic and algebraic manipulation.
Common mistakes
Confusing the conversion factors (using 180/π instead of π/180 and vice-versa).
Assuming π = 22/7 for radian measures without considering the context (π is an irrational number).
Incorrectly applying the formulas for arc length or sector area using the wrong angle unit.
Practice preview
Convert 2pi/3 radians to degrees.…
easy
Which of the following statements correctly represents the fundamental relationship between degrees and radians?…
easy
An arc of length 11 cm subtends an angle at the centre of a circle of radius 14 cm. Find the angle in radians.…
medium