6.1: angles and their measure
DESCRIPTION
6.1: Angles and their measure. January 5, 2008. Objectives. Learn basic concepts about angles Apply degree measure to problems Apply radian measure to problems Calculate arc length Calculate the area of a sector. What is an angle?. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/1.jpg)
6.1: Angles and their measure
January 5, 2008
![Page 2: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/2.jpg)
Objectives
• Learn basic concepts about angles• Apply degree measure to problems• Apply radian measure to problems• Calculate arc length• Calculate the area of a sector
![Page 3: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/3.jpg)
What is an angle?• An angle is formed by
rotating a ray around its end point.
• Important terms:– Initial side: starting
position of the ray– Terminal side: the final
position of the ray– Positive measure: ray is
rotated counterclockwise– Negative measure: ray is
rotated clockwise
![Page 4: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/4.jpg)
Degree measure• One complete rotation
is 360°.• 90° is a right angle.• 180° is a straight
angle.• Symbols used to
denote angles:– Alpha - α– Beta - β– Theta - θ
![Page 5: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/5.jpg)
Important angle terms• Complementary angles
add to be 90°.• Supplementary angles
add to be 180°.• Acute angles 0<θ<90.• Obtuse angles
90<θ<180.• Coterminal angles:
angles with the same terminal side.
![Page 6: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/6.jpg)
Radian measure• The circumference of a
circle is 2π.• Therefore, one rotation of
ray is 2π radians.• To convert from degrees to
radians..Multiply degrees by π/180°
• To convert from radians to degrees..Multiply radians by 180°/π
• 2π = 360°• π = 180°• π/2 = 90°• π/3 = 60°• π/4 = 45°• π/6 = 30°
![Page 7: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/7.jpg)
Try these
Degree to radian120°
150°
200°
320°
Radian to degree2π/5
3π/4
7π/5
6π/5
![Page 8: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/8.jpg)
Arc length• Arc length
s= rθ• θ must be in radian
measure.
![Page 9: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/9.jpg)
Try it
A circle has a radius of 4. Find the length of an arc intercepted by a central angle of 60°.
![Page 10: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/10.jpg)
Try this one
A circle has a radius of 12. The arc length of a certain angle is 4. Find the central angle.
![Page 11: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/11.jpg)
Area of a sector• Area of a sector
A= (1/2)r2 θ• θ must be in radian
measure.
![Page 12: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/12.jpg)
Try it
A circle has a radius of 5. Find the area of the sector if the central angle is 75°.
![Page 13: 6.1: Angles and their measure](https://reader035.vdocument.in/reader035/viewer/2022062520/568161dc550346895dd1eb9b/html5/thumbnails/13.jpg)
Your assignment
1,2 – sketching angles21-26 – complementary and supplementary35-38 – find the central angle43, 44 – converting from degrees to radians47-52 – find the missing value (arc length)65-68 – area of a sector