1. T1.1a To Define Angles and To Add, Subtract in DMS
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T1.1a To Define Angles and To Add, Subtract in DMS

2. * LESSON: How would you describe an angle? terminal side angle vertex
initial side
We will be looking at angles on the “Unit Circle” (a circle whose radius is one unit and usually on the Cartesian coordinate system. Actually, it does not matter how big or small it is, because all circles are similar.)

3. 0°, 90°, 180°, 270°, & 360° are: QUADRANGLE ANGLES.
Here’s a unit circle. y
It has x and y axes: II I
90°
It has quadrants:
180° 0° x
360°
0°, 90°, 180°, 270°, & 360° are: QUADRANGLE ANGLES.
270°
III IV

4. In which quadrants would you find: 148°, 332°, 400°, & -102°?
Angles in Standard Position: Measured from the initial side on the positive x axis to the terminal side. II I
90°
180° 0° x
360°
In which quadrants would you find: 148°, 332°, 400°, & -102°?
270°
III IV

5. How would you define one degree?
What have we learned? II I
You can have more than one rotation and you can rotate in a negative direction
90°
180° 0°
360°
Angles move counter clockwise for positive angles and clockwise for negative angles
270°
III IV
How would you define one degree?

6. * ʺ is the symbol for seconds ´ is the symbol for minutes Definitions:
Degree: 1/360th of a circle
´ is the symbol for minutes
Minute: 1/60th of a degree
ʺ is the symbol for seconds
Second: 1/60th of a minute
These are conversion units—KNOW THEM!!!
1 r (rotation or revolution) = 360°

7. This measurement is called DMS (degrees minutes seconds).
Like time, it comes from the ancient Babylonians, whose base unit was 60!
For example:
Is read: 42 degrees, 15 minutes, 35 seconds
Why would we need to divide a degree into such small units?

8. I. When adding DMS, add degrees together, minutes together, and seconds together. (USE BABY CALC’S)
For example:
But, what about:
???

9. Try:
Try:

10. II. Let’s try subtraction:
What about:

11. Active Learning Assignment:
Handout on DMS Add & Subtract Do Columns 1 & 2
WOW:
“Anything that you do for 28 days straight become a habit—for good or bad!”