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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)
