Lesson 5-1 Angles and Degree Measure
Objectives: ­ Convert decimal degree measures to degrees, minutes and seconds and vice versa. ­ Find the number of degrees in a given number of rotations.
­ Identify Coterminal angles.
­ Understand how reference angles work
How do we know our location in the world right now?
What ways are there to measure our location?
To change degree, min and seconds into just a degree we have to remember a few things: 3600 in a circle and a 300 angle is 1/12 of a complete rotation. 1': 1 min 1": 1 sec 10 = 60 mins
1 min = 60 secs
10 = 3600 sec
How would you change this to just degrees?
Calculator check: 43 2nd APPS 0 13 2nd APPS '
43 Alpha " (the + key) ENTER
To change it back 43.228611
Multiply the decimal portion by 60 to get minutes
Multiply the decimal potion by 60 to get the seconds
.226611 times 60 = 13.71666
.71666 times 60 = 43
Calculator:
To change it back Enter 43.228611
2nd APPS DMS
Enter Try These: 1. Change 329.1250 to deg, min, sec
2. Change to a decimal rounded to the nearest thousandth. Quick Reminder: Label the quadrants Notes:
l na
mi
e
Sid
r
Te
Initial Side
Initial Side: Is Fixed
Terminal Side: Rotates around the vertex
An angle's measure tells us:
1. The amount of rotation from initial to teminal
2. The direction of the rotation
­ counterclockwise is positive
­ clockwise is negative
Standard Position: Vertex at origin initial side on positive x axis. If the terminal side of an angle in standard position coincides with one of the axes, the angle is called a quadrantal. Give the angle measure represented by each rotation: 1. 4.5 rotations clockwise
2. 3.3 rotations counterclockwise Coterminal Angles: Two angles in standard position that share the same terminal side.
Positive Coterminal Angles: 70 + 360(1) = 430 degrees
Negative Coterminal Angles
70 ­ 360 (1)= ­290
How can you verify that your angles are coterminal? Find a coterminal angle that is betweeen 00 and 3600. What quadrant is the terminal side in?
a. 7750 b. ­12970 Identify all angles that are coterminal with each angle. Then find one positive angle and one negative angle that are coterminal with the angle. 1. 860 2. 2940
If each angle is in standard position, determine a coterminal angle that is between 0 and 360. State the quadrant in which the terminal side lies. 3. 5950
4. ­7770 Reference angle: acute angle formed by the terminal side of the given angle and the x­
axis. Homework: 18­57 by 3's, 58, 59, 63, 65