Angles and their measures

Chapter 4 Angles and their measuresDegrees vs RadiansWhat do you know about degrees?

What do you know about Radians?DegreesExample:How to do it for A:How to do it for B:NavigationIn navigation, the course or bearing of an object is sometimes given as the angle of the line of travel measured clockwise from due north.Slide 4- 7What is Radian? A central angle of a circle has measure 1 radian if it intercepts an arc with the same length as the radius.

Slide 4- 8

Degree-Radian Conversion Slide 4- 9

Example Working with Radian MeasureHow many radians are in 60 degrees?Slide 4- 10AnswerGroup Work:Arc Length Formula (Radian Measure) Slide 4- 13

Arc Length Formula (Degree Measure) Slide 4- 14

Note:So basically, when you find the arc length of a circle, you are finding the radian!!Example Perimeter of a Pizza Slice Slide 4- 16

Example Perimeter of a Pizza Slice Slide 4- 17

Angular and Linear MotionAngular speed is measured in units like revolutions per minute.Linear speed is measured in units like miles per hour.Slide 4- 18Example:You have a car, its wheels are 36 inches in diameter. If the wheels are rotating at 630 rpm, find the trucks speed in miles per hourAnswerNautical MileA nautical mile (naut mi) is the length of 1 minute of arc along Earths equator.Slide 4- 21

Statute mileStatue mile is the land mileDistance Conversions Slide 4- 23

ExampleFrom Boston to San Franciso is 2698 stat mi, convert it to nautical mile.AnswerHomework PracticeP 356 #1-39 every other oddTrigonometric Functions, special right triangles and the unit circleDay 1Exploration activity!

You are to cut out the unit circle I provided onto the notebook.

You are to trace as many special right triangle onto the unit circle as possible, but here is the rule. The hypotenuse of the triangle must be the radius of the circle and one leg on the axis.

Hint: You should have 3 per quadrant

After tracing it all, find the coordinates of the points that lies right on the circle and find the cumulative degrees of each point on the circle. Then answer the following questions in your group28Slide 4- 29Result from the activity should be like this:

Day 1Why is it called a unit circle?

How does the special right triangles and unit circle relate? What does the special right triangles give you relating to the circle?

Is it possible to convert the degrees into radians? How do you do it?Slide 4- 31Unit CircleThe unit circle is a circle of radius 1 centered at the origin.

ReviewPractice*Teacher make up different problems regarding SOHCAHTOANote:Practice Using Unit Circle*Teacher make up different practices regarding Unit CircleTrigonometry Extension

PracticeTeacher make up different practices regarding the 6 trigonometry functionsSlide 4- 38Initial Side, Terminal Side

Slide 4- 39Positive Angle, Negative Angle

Slide 4- 40Coterminal AnglesTwo angles in an extended angle-measurement system can have the same initial side and the same terminal side, yet have different measures. Such angles are called coterminal angles.Slide 4- 41Example Finding Coterminal Angles

Slide 4- 42Example Finding Coterminal Angles

Slide 4- 43Example Finding Coterminal Angles

Slide 4- 44Example Evaluating Trig Functions Determined by a Point in QI

Slide 4- 45Example Evaluating Trig Functions Determined by a Point in QI

Slide 4- 46Example Evaluating More Trig Functions

Slide 4- 47Example Using one Trig Ration to Find the Others

Homework PracticeP 366 #1-55 EOO

P 381 #1-48 EOESolving Trig FunctionsFunction and its inverseVery Important notePractices with inverses*Teacher make up different problemsHomework PracticePg 421 #1-32 EOO, 47,54Graphing Sin, Cos and TanActivityRelate back to transformations:Slide 4- 57Sinusoid

Slide 4- 58Amplitude of a Sinusoid

Slide 4- 59Period of a Sinusoid

Slide 4- 60Example Horizontal Stretch or Shrink and Period

Slide 4- 61Example Horizontal Stretch or Shrink and Period

Slide 4- 62Frequency of a Sinusoid

Slide 4- 63Example Combining a Phase Shift with a Period Change

Slide 4- 64Example Combining a Phase Shift with a Period Change

Slide 4- 65Graphs of Sinusoids

Slide 4- 66Constructing a Sinusoidal Model using Time

Homework PracticeP 392 #1-52 EOEGraphs of Tangent, Cotangent, Secant, and CosecantTangent Graph

QuestionWhy are there vertical asymptotes?Cotangent Graph

QuestionWhy are there vertical asymptotes?Group WorkGraph y=cos x Secant Graph

Group WorkGraph y = sin xCosecant Graph

SolveHomework PracticePg 402 #17-34