U1L02P1FST Part B – Unit 1 Lesson 02 Radian and Degree Measure

Lesson 2: Radian and Degree Measure :

Lesson 2: Radian and Degree Measure Essential Questions for this Lesson:
How does Degree Measure compare to Radian Measure?
What is the procedure to convert from Radians to Degrees and from Degrees to Radians?

What is a “radian”? :

What is a “radian”? Wikipedia definition:
The radian is a unit of plane angle, equal to 180/π (or 360/(2π)) degrees, or about 57.2958 degrees, or about 57°17′45″. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level.
The radian is represented by the symbol "rad" or, more rarely, by the superscript c (for "circular measure"). For example, an angle of 1.2 radians would be written as " 1.2 rad " or " 1.2c " (the second symbol is often mistaken for a degree: " 1.2° "). However, the radian is mathematically considered a "pure number" that needs no unit symbol, and in mathematical writing the symbol "rad" is almost always omitted. In the absence of any symbol radians are assumed, and when degrees are meant the symbol ° is used.

How does radian measure compare to arclength? :

How does radian measure compare to arclength? The standard introduction to radian measure and unit circle trigonometry involves "wrapping" the real t number line around the unit circle with equation x2 + y2 = 1. This Demonstration illustrates that wrapping. The number line is wrapped with integer radian values and then also in terms of /2. The t number line is colored to enhance the visual understanding of which numbers end up where on the unit circle.

Example: Draw a figure depicting an angle of 2/3. :

Example: Draw a figure depicting an angle of 2/3. Initial Leg on x-axis
LABELS!
Direction Matters!
(-) clockwise
(+) counter-clockwise
Terminal Leg (PRACTICE!) θ = 2/3 x y

Practice for radian measures… :

Practice for radian measures… Polar angles and points on the unit circle (Wolfram Demonstration Project application)
Converting Radians to Degrees
Adegrees = Aradians * 180°/
Aradians = Adegrees * /180° Convert /4 to degrees:
Adegrees = Aradians * 180°/
A = /4 * 180°/
A = 45° Convert 120° to radian measure:
Aradians = Adegrees * /180°
A = 120° * /180°
A = 2/3 (or 2/3 radians)

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