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

Acute Angles An 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 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

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

Rotations Clockwise Counterclockwise

Clockwise MOVEMENT GIVES A NEGATIVE ANGLE -60°

Counterclockwise MOVEMENT GIVES A POSITIVE ANGLE 60°

REMEMBER ANGLE MEASURE IS ALWAYS POSITIVE NEGATIVE TELLS DIRECTION

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° 1200° -120° III I II IV II IV III II

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 + 360 = 390° 30° 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° 30 - 360 = -330° -330 - 360 = -690° 30° -690 - 360 = -1050° HINT: TO GET BACK TO SAME PLACE YOU MUST GO ALL THE WAY AROUND IN THE POSITIVE DIRECTION OR NEGATIVE DIRECTION

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

Pythagorean Theorem and Distance 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 rotation 8. ½ clockwise rotation 9. 1/6 counterclockwise rotation 10. 3/8 counterclockwise rotation 11. 19/12 counterclockwise rotation