Angles and Degree Measure

ANGLES AND DEGREE MEASURESection 12-1

Pages 549-554

Angles and Degree Measure

• Trigonometry• Literally means “triangle measurement”• Used in surveying, navigation, architecture, etc.• For the next few months we will be working with mainly triangles

Angles and Degree Measure

• Angle measurements• Given in degrees• One degree (1°) is of a complete rotation • In trigonometry, you work with angles greater than 180°

as well as negative angles (< 0°)

Angles and Degree Measure

Positive Angles

• Move counterclockwise

Negative Angles

• Move Clockwise

Initial Side

Terminal Side Initial Side

Terminal Side

Angles and Degree Measure

• An angle in standard position:1) Initial Side on the x-axis

2) Vertex is at the origin

• First quadrant angle:

II I

III IV

Angles and Degree Measure

• An angle in standard position:1) Initial Side on the x-axis

2) Vertex is at the origin

• Second quadrant angle:

II I

III IV

Angles and Degree Measure

• An angle in standard position:1) Initial Side on the x-axis

2) Vertex is at the origin

• Third quadrant angle:

II I

III IV

Angles and Degree Measure

• An angle in standard position:1) Initial Side on the x-axis

2) Vertex is at the origin

• Fourth quadrant angle:

II I

III IV

Angles and Degree Measure

• There are also an infinite number of quadrantal angles• Angles whose terminal side lies on a set of axis

II I

III IV

Angles and Degree Measure

• There are also an infinite number of quadrantal angles• Angles whose terminal side lies on a set of axis

II I

III IV

Angles and Degree Measure

• Coterminal angles• Two angles that have the same:

1) Initial Side

2) Terminal Side

3) Vertex

• What other coterminal angles does 150° have?

150°

-210°

Angles and Degree Measure• Write a formula for the measures of all the angles

coterminal with a 30° angle.

30°

Angles and Degree Measure• Write a formula for the measures of all the angles

coterminal with a 270° angle.

270°

ANGLES AND DEGREE MEASURESection 12-1

Pages 549-554

Angles and Degree Measure

• Minutes and Seconds• Measure angles more precisely• Similar to decimal degrees

• 1 minute (1') is of 1°• 1 second (1'') is of 1'

= of 1°

Angles and Degree Measure

• Express 14°36'54'' in degrees:

¿14+¿3660543600+¿

¿14.615 °

Angles and Degree Measure

• Express 72.568° in degrees, minutes, and seconds. (.568 x 60)'

34.08 34' +(.08 x 60)''4 .8 34' 5''

Angles and Degree Measure

• Try the following:

a) Express 64°9‘36'' as a decimal

b) Express 53.721° in degrees, minutes, & seconds 43' 16''¿64.16 °

Angles and Degree Measure

• Oral Exercises• Page 551

Angles and Degree Measure

• Find a first quadrant angle θ for which an angle four times as large will be in the second quadrant.

Angles and Degree Measure

• Find a first quadrant angle θ for which an angle six times as large is in the third quadrant.

Angles and Degree Measure

• Today:• Angles in standard position• Coterminal angles• Converting between degrees and degrees, minutes, & seconds

Angles and Degree Measure

• Written Exercises• 31-45 odd and 55 - 65(page 552)