Презентация, доклад по математике на тему Radian and Degree Measure

following topics:
Terminology used to describe angles
Degree measure of an angle
Radian measure of an angle
Converting between radian and degree measure
Find coterminal angles

an angle in standard position is always located on the positive x-axis.

use an arrow to show direction.

determined by the amount of rotation from the initial side to the terminal side.

There are two common ways to measure angles, in degrees and in radians.
We’ll start with degrees, denoted by the symbol º.
One degree (1º) is equivalent to a rotation of of one revolution.

terminal sides lie.

Ex1: Name the quadrant in which each angle lies.
50º
208º II I
-75º III IV

6.1 Radian and Degree Measure

Classifying Angles

Quadrant 1

Quadrant 3

Quadrant 4

terminal side on one of the axes are called quadrantal angles.
For example, 0º, 90º, 180º, 270º, 360º, … are quadrantal angles.

and terminal sides are coterminal.

Angles α and β are coterminal.

an angle that is coterminal to a given angle θ by adding or subtracting multiples of 360º.

Ex 2: Find one positive and one negative angle that are coterminal to 112º.

For a positive coterminal angle, add 360º : 112º + 360º = 472º
For a negative coterminal angle, subtract 360º: 112º - 360º = -248º

coterminal with the angle θ = 30° in standard position.

Ex 4. Find one positive and one negative angle that is coterminal with the angle θ = 272° in standard position.

is in radians.

Definition of Radian:
One radian is the measure of a central angle θ that intercepts arc s equal in length to the radius r of the circle.

In general,

to radians, multiply degrees by

To convert radians to degrees, multiply radians by

30°

-54°

-118°

45°

coterminal with the angle θ = in standard position.

Ex 8. Find one positive and one negative angle that is coterminal with the angle θ = in standard position.

that are coterminal with the given angle.
135°