This document discusses radians and degree measures of angles. Some key points: - A radian is the measure of a central angle that intercepts an arc equal in length to the radius of the circle. There are 2π radians in a full circle. - Coterminal angles have the same initial and terminal sides and can be obtained by adding or subtracting full revolutions (2π) to an angle measure. - The document provides examples of converting between degrees and radians and finding coterminal angles.

1. 4.1 Radian and Degree
Measures
Essential Question:
What is a "radian" and how do you convert to and from
radians?
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2. Warm-up:
Classify the following angles:
How many degrees in a full circle?
Find the circumference of the circle below.
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3. 4.1 Radian and Degree Measure
Parts of every angle:
­Initial Side (ray)
­Terminal Side (ray)
­Vertex
Standard Position:
­Initial side on the _______
­Vertex on the _______
+ angles: ________
– angles: ________
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4. Coterminal Angles: Angles that have the
same ________ and ________ sides.
Naming an angle:
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5. Radians Video
A radian is the measure of a central angle
that intercepts an arc equal in length to the
radius of the circle.
How many radians in 1
full circle?
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6. The Ratio:
Ex. 1) Convert the following to degrees or
radians.
a) 135° b) 320°
c)–5π/3 d) π/6
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7. The Quadrants
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8. Coterminal Angles Revisited
Since coterminal angles have the same initial and
terminal sides, when an angle is in standard position you
can adding/subtracting a "revolution" to the angle will
give you a new angle in the same position.
Ex. 2) Find two angles
that are coterminal
with 9π/4.
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9. Assignment:
4.1A p. 290 #3-69
(mult. of 3)
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