1. Angles in the Coordinate Plane
Standard Position
Quadrantal Angles
Coterminal Angles
Sketching Angles

2. Acute Angles
An acute angle is an angle measuring between 0 and 90 degrees.

3. Obtuse Angles
An obtuse angle is an angle measuring between 90 and 180 degrees.

4. Right Angles
A right angle is an angle measuring 90 degrees.

5. Complementary Angles
Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees.

6. These two angles are complementary because when you put them together you get a 90 degree angle.

7. Supplementary Angles
Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees.

8. These two angles are supplementary because when you put them together you get a 180 degree angle. Or a Straight line.

9. Standard Position
Terminal Side
INITIAL SIDE OF THE ANGLE LIES ON THE POSITIVE HALF OF THE X-AXIS AND THE VERTEX IS AT THE ORIGIN. THE TERMINAL SIDE DETERMINES THE QUADRANT AN ANGLE LIES IN
Origin
Initial side

10. QUADRANTAL ANGLES
AN ANGLE IN STANDARD POSITION WHOSE TERMINAL SIDE FALLS ON THE X OR Y AXIS. 0°, 90°, 180°, 270°, 360°, 450°, 540°, 630°, 720°…
ONE ROTATION IS 360°. TWO = 720°, THREE = 1080°, ETC
TO DRAW A BIG ANGLE LIKE 850° --- SPIRAL

11. Rotations
Clockwise
Counterclockwise

12. Clockwise
MOVEMENT GIVES A NEGATIVE ANGLE
-60°

13. Counterclockwise
MOVEMENT GIVES A POSITIVE ANGLE
60°

14. REMEMBER
ANGLE MEASURE IS ALWAYS POSITIVE
NEGATIVE TELLS DIRECTION

15. Q III I II IV II IV III II 220° 400° 900° -200° -750° 110°
EXAMPLE: TELL WHAT QUADRANT EACH ANGLE WOULD LIE IN OR STATE THAT IT IS QUADRANTAL Q
220° 400° 900°
-200° -750° 110°
650° ° -120°
III I II IV II IV
III II

16. Name the Measure and Sketch
2/3 ROTATION COUNTERCLOCKWISE
7/6 ROTATION CLOCKWISE
240°
-420°

17. Coterminal Angles ANGLES THAT SHARE THE SAME TERMINAL SIDE
MUST DIFFER BY WHOLE ROTATION ± 360°

18. NAME 3 POSITIVE ANGLES THAT ARE COTERMINAL WITH 30°
= 390°
30°
= 750°
= 1110°
HINT: TO GET BACK TO SAME PLACE YOU MUST GO ALL THE WAY AROUND IN THE POSITIVE DIRECTION OR NEGATIVE DIRECTION

19. NAME 3 NEGATIVE ANGLES THAT WOULD BE COTERMINAL WITH 30°
= -330°
= -690°
30°
= -1050°
HINT: TO GET BACK TO SAME PLACE YOU MUST GO ALL THE WAY AROUND IN THE POSITIVE DIRECTION OR NEGATIVE DIRECTION

20. Homework
pg. 7-9
# 2-8 even, 14,16,17, 89,90, odd

22. Pythagorean Theorem and Distance Formula
Classwork: Handout
Homework: pg. 7-9
# 2-8 even, 14,16,17, 89,90, odd

23. *Use the Pythagorean Theorem to find each indicated length.
1. AC =12, BC = 5, AB = ?
2. AC = 5, BC = 5, AB = ?
3. AB = 4√3, BC = 2√3, AC =?
*Find the distance between each of the pairs of points.
4. A(-5,4); B(3,-2)
5. C(-2,3); D(-4,-1)
6. K(4,-4);L(-10,3)
*For each of the rotations find the degree measure of the angle and then sketch the angle in standard position.
7. ¼ clockwise rotation
8. ½ clockwise rotation
9. 1/6 counterclockwise rotation
10. 3/8 counterclockwise rotation
11. 19/12 counterclockwise rotation