Warm up for 8.5Warm up for 8.5

Compare the ratios sin A and cos B

Compare the ratios sec A and csc B

Compare the ratios tan A and cot B

pg 618

At an altitude of 1,000 ft., a balloonist measures the angle of depression from the balloon to the landing zone. The

measure of the angle is 15 degrees. How far is the balloon from the landing zone?

Angle of Depression Pg 622

3

Radian and Degree MeasureRadian and Degree Measure

In this section, we will study the 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

Lots of room for notes on 623

Radian and Degree MeasureRadian and Degree Measure

4

Angles

Trigonometry: measurement of triangles

Angle Measure

Radian and Degree MeasureRadian and Degree Measure

5

Standard Position

Vertex at origin

The initial side of an angle in standard position is always located on the positive x-axis.

Radian and Degree MeasureRadian and Degree Measure

6

Positive and negative angles

When sketching angles, always use an arrow to show direction.

Radian and Degree MeasureRadian and Degree Measure

7

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.

1

360

Radian and Degree MeasureRadian and Degree Measure

8

Measuring Angles

1

360

Radian and Degree MeasureRadian and Degree Measure

9

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

Classifying Angles

Quadrant 1

Quadrant 3

Quadrant 4

Radian and Degree MeasureRadian and Degree Measure

10

Classifying Angles

Standard position angles that have their terminal side

on one of the axes are called quadrantal angles.

For example, 0º, 90º, 180º, 270º, 360º, … are

quadrantal angles.

Radian and Degree MeasureRadian and Degree Measure

11

Radian Measure

A second way to measure angles is in radians.

Definition of Radian:

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

s

r

In general,

Radian and Degree MeasureRadian and Degree Measure

12

Radian Measure

2 radians corresponds to 360

radians corresponds to 180

radians corresponds to 902

2 6.28

3.14

1.572

Radian and Degree MeasureRadian and Degree Measure

13

Radian Measure

Radian and Degree MeasureRadian and Degree Measure

14

Conversions Between Degrees and Radians

1. To convert degrees to radians, multiply degrees by

2. To convert radians to degrees, multiply radians by

180

180

Ex 5. Convert the degrees to radian Ex 5. Convert the degrees to radian measure.measure.

a) 60

b) 30

c) -54

d) -118

e) 45

Ex 6. Convert the radians to degrees.Ex 6. Convert the radians to degrees.

a)

b)

c)

d)

6

2

11

18

9

17

0°

360 °

30 °

45 °

60 °

330 °

315 °

300 °

120 °

135 °

150 °

240 °

225 °

210 °

180 °

90 °

270 °

Degree and Radian Form of “Special” Angles

Class WorkClass Work

Convert from degrees to radians.1.542.-300

Convert from radians to degrees.3.

4.

11

3

13

12

8.5 and 8.5 and Angles and Angle Measure Angles and Angle Measure

WorksheetWorksheet

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