Moving from Degrees to Radians: Conversion between Degrees and Radians YouTube Lecture Handouts
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Topics
- What is a radian?
- Advantages of Measuring and “Thinking” in Radians
- Conversion from Radians to Degrees
- Conversion from Degrees to Radians
- Conversion Tables
What is a Radian?
- Angle subtended by an arc at the center in radians is the ratio of arc length to radius.
- 1 radian is the angle for which the arc length is one radius.
- The circumference is π diameters and radii, so one complete revolution is radians.
- Traditionally a circle was divided into 360 degrees since that number has a convenient list of factors, and so one radian is degrees.
Always Think in Radians Not 360 Degrees
- Radian is most natural unit to measure angles.
- Algebraic expansion of trigonometric functions. .
- Calculus! !
Degrees were used because 360 has lot of factors and so easy to divide the circle into equal portions
Converting from Radians to Degrees
- radians = 360 degrees
- 1 radian = degrees
- 360 degrees radians
- 1 degree = radians
Convert 90 degrees to radians.
Convert into degrees (30 degrees)
Convert -150 degrees to radians
Convert
Problem
In a circle with radius 6 cm, what is the measure (in degrees) of an arc whose length is cm
Some Common Conversions
✍ Mayank