Radian and degree measure.

TRIGNOMETRIC FUNCTIONS

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Radian and Degree Measure

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Angle- formed by rotating a ray about its endpoint (vertex)

Initial Side Starting position

Terminal Side Ending position

Standard Position

Initial side on positive x-axis and the vertex is on the origin

Angle describes the amount and direction of rotation120° –210°

Positive Angle- rotates counter-clockwise (CCW)

Negative Angle- rotates clockwise (CW)

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6.1 Radian and Degree Measure

Measuring Angles

The measure of an angle is 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.

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360

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6.1 Radian and Degree Measure

Measuring Angles

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360

Degrees, Minutes and Seconds

One complete revolution = 360± One minute:

One-sixtieth of a degree One minute is denoted 10

1O = 60

One second: One-sixtieth of a minute One second is denoted 100

10 = 6000

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Angles are often classified according to the quadrant

in which their 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

Basic Terminology

Quadrantal angle: Angle in standard position that doesn’t lie in any quadrant

Lies in quadrant II

Lies in quadrant IV

Quadrantal angle

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6.1 Radian and Degree Measure

Coterminal Angles

Angles that have the same initial and terminal sides are

coterminal.

Angles and are coterminal.

Coterminal Angles: Two angles with the same initial and terminal sides

Find a positive coterminal angle to 20º

38036020

34036020Find a negative coterminal angle to 20

Radians

Central angle: An angle whose vertex is at the center of a circle Central angles subtend an arc on the circle

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Definition of a Radian

A radian is the angle subtended at the centre of a circle by an arc whose length is equal to the radius of a circle.

RadiansAngle subtended at the centre by an arc of

length 1unit in a unit circle is said to have a measure of 1 radian.

The Radian

1 radian ≈ 57.3o 2 radians ≈ 114.6o 3 radians ≈ 171.9o

4 radians ≈ 229.2o 5 radians ≈ 286.5o 6 radians ≈ 343.8o

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6.1 Radian and Degree Measure

Radian Measure

2 radians corresponds to 360

radians corresponds to 180

radians corresponds to 902

2 6.28

3.14

1.572