Unit 5 Vocab By: Gus Koza. Acute angle An angle that is less than 90 degrees.
An acute angle is an angle measuring between 0 and 90 degrees.
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Transcript of An acute angle is an angle measuring between 0 and 90 degrees.
![Page 1: An acute angle is an angle measuring between 0 and 90 degrees.](https://reader036.fdocuments.net/reader036/viewer/2022081501/5697bff41a28abf838cbd022/html5/thumbnails/1.jpg)
Angles in the Coordinate Plane
Standard PositionQuadrantal AnglesCoterminal AnglesSketching Angles
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Acute AnglesAn acute angle is an angle measuring between 0 and 90 degrees.
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Obtuse Angles
An obtuse angle is an angle measuring between 90 and 180 degrees.
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Right Angles
A right angle is an angle measuring 90 degrees.
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Complementary Angles
Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees.
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These two angles are complementary because when you put them together you get a 90 degree angle.
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Supplementary Angles
Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees.
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These two angles are supplementary because when you put them together you get a 180 degree angle. Or a Straight line.
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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
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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
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RotationsClockwiseCounterclockwise
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Clockwise
MOVEMENT GIVES A NEGATIVE ANGLE
-60°
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CounterclockwiseMOVEMENT GIVES A POSITIVE ANGLE
60°
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REMEMBERANGLE MEASURE IS ALWAYS POSITIVENEGATIVE TELLS DIRECTION
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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
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Name the Measure and Sketch
2/3 ROTATION COUNTERCLOCKWISE
7/6 ROTATION CLOCKWISE
240°
-420°
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Coterminal Angles
ANGLES THAT SHARE THE SAME TERMINAL SIDE
MUST DIFFER BY WHOLE ROTATION ± 360°
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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
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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°
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Homeworkpg. 7-9# 2-8 even,
14,16,17, 89,90,103-113 odd
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Pythagorean TheoremandDistance Formula
Classwork: Handout Homework: pg. 7-9# 2-8 even, 14,16,17, 89,90,103-113 odd
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*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