Angles in the Coordinate Plane

Standard PositionQuadrantal AnglesCoterminal AnglesSketching Angles

Acute AnglesAn acute angle is an angle measuring between 0 and 90 degrees.

Obtuse Angles

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

Right Angles

A right angle is an angle measuring 90 degrees.

Complementary Angles

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

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

Supplementary Angles

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

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

Standard PositionINITIAL 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

Terminal Side

Initial side

Origin

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

QUADRANTAL ANGLES

RotationsClockwiseCounterclockwise

Clockwise

MOVEMENT GIVES A NEGATIVE ANGLE

-60°

CounterclockwiseMOVEMENT GIVES A POSITIVE ANGLE

60°

REMEMBERANGLE MEASURE IS ALWAYS POSITIVENEGATIVE TELLS DIRECTION

EXAMPLE: TELL WHAT QUADRANT EACH ANGLE WOULD LIE IN OR STATE THAT IT IS QUADRANTAL

220° 400° 900°

-200° -750° 110°

650° 1200° -120°

III

II

IV

I

IV

Q

II

II

III

Name the Measure and Sketch

2/3 ROTATION COUNTERCLOCKWISE

  7/6 ROTATION CLOCKWISE

240°

-420°

Coterminal Angles

ANGLES THAT SHARE THE SAME TERMINAL SIDE

MUST DIFFER BY WHOLE ROTATION ± 360°

NAME 3 POSITIVE ANGLES THAT ARE COTERMINAL WITH 30°

30°

30 + 360 = 390°

390 + 360 = 750°

750 + 360 = 1110°

HINT: TO GET BACK TO SAME PLACE YOU MUST GO ALL THE WAY AROUND IN THE POSITIVE DIRECTION OR NEGATIVE DIRECTION

NAME 3 NEGATIVE ANGLES THAT WOULD BE COTERMINAL WITH 30°

HINT: TO GET BACK TO SAME PLACE YOU MUST GO ALL THE WAY AROUND IN THE POSITIVE DIRECTION OR NEGATIVE DIRECTION

30°

-330 - 360 = -690°

30 - 360 = -330°

-690 - 360 = -1050°

Homeworkpg. 7-9# 2-8 even,

14,16,17, 89,90,103-113 odd

Pythagorean TheoremandDistance Formula

Classwork: Handout Homework: pg. 7-9# 2-8 even, 14,16,17, 89,90,103-113 odd

*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 rotation8. ½ clockwise rotation9. 1/6 counterclockwise rotation10. 3/8 counterclockwise rotation11. 19/12 counterclockwise rotation