sullivan algebra and trigonometry section 7 1 angles and their measures l.
Download
Skip this Video
Download Presentation
Sullivan Algebra and Trigonometry: Section 7.1 Angles and Their Measures

Loading in 2 Seconds...

play fullscreen
1 / 18

Sullivan Algebra and Trigonometry: Section 7.1 Angles and Their Measures - PowerPoint PPT Presentation


  • 151 Views
  • Uploaded on

Sullivan Algebra and Trigonometry: Section 7.1 Angles and Their Measures. Objectives of this Section Convert Between Degrees, Minutes, Seconds, and Decimal Forms for Angles Convert From Degrees to Radians, Radians to Degrees Find the Arc Length of a Circle

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Sullivan Algebra and Trigonometry: Section 7.1 Angles and Their Measures' - diem


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
sullivan algebra and trigonometry section 7 1 angles and their measures
Sullivan Algebra and Trigonometry: Section 7.1Angles and Their Measures
  • Objectives of this Section
  • Convert Between Degrees, Minutes, Seconds, and Decimal Forms for Angles
  • Convert From Degrees to Radians, Radians to Degrees
  • Find the Arc Length of a Circle
  • Find the Area of a Sector of a Circle
slide2

A ray, or half-line, is that portion of a line that starts at a point V on the line and extends indefinitely in one direction. The starting point V of a ray is called its vertex.

V

Ray

slide3

If two lines are drawn with a common vertex, they form an angle. One of the rays of an angle is called the initial side and the other the terminal side.

Terminal side

Initial Side

Vertex

Counterclockwise rotation

Positive Angle

slide4

Terminal side

Vertex

Initial Side

Clockwise rotation Negative Angle

Terminal side

Vertex

Initial Side

Counterclockwise rotation Positive Angle

slide5

y

Terminal side

x

Vertex

Initial side

slide6

y

x

When an angle is in standard position, the terminal side either will lie in a quadrant, in which case we say lies in that quadrant, or it will lie on the x-axis or the y-axis, in which case we say is a quadrantal angle.

y

x

slide7

Angles are commonly measured in either Degrees or Radians

The angle formed by rotating the initial side exactly once in the counterclockwise direction until it coincides with itself (1 revolution) is said to measure 360 degrees, abbreviated

Terminal side

Initial side

Vertex

slide8

Terminal side

Vertex

Initial side

slide9

Terminal side

Vertex

Initial side

slide10

y

Vertex

Initial side

x

Terminal side

slide14

Consider a circle of radius r. Construct an angle whose vertex is at the center of this circle, called the central angle, and whose rays subtend an arc on the circle whose length is r. The measure of such an angle is 1 radian.

r

1 radian

slide15

For a circle of radius r, a central angle of radians subtends an arc whose length s is

Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 2 radians.

slide16

The area A of the sector of a circle of radius r formed by a central angle measured in radians is

Example: Find the area of the sector of the circle of radius 4 inches formed by an angle of 45 degrees.