Young Trig 3e Chapter3 PPT

8/11/2019 Young Trig 3e Chapter3 PPT

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Chapter 3

Overview


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Chapter 3

Objectives

Convert between degrees and radians.

Calculate arc length and the area of a circular sector.

Relate angular and linear speeds.

Draw the unit circle and label the sine and cosine valuesfor special angles (in both degree and radians.)


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Section 3.1

Radian Measure

Skills Objectives

Calculate the radian

measure of an angle.

Convert between degreesand radians.

Calculate trigonometric

function values for angles

given in radians.

Conceptual Objectives

Understand that degrees

and radians are both

measures of angles. Realize that radian

measure allows us to write

trigonometric functions as

functions of real numbers.


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Radian Measure

To correctly calculate radians from the

formula , the radius and arc length

must be expressed in the same units.

=

s

r


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Your Turn: Calculate Radian Measure

What is the measure (in radians) of a central

angle that intercepts an arc of length 12 mm

on a circle with radius 4 cm?Solution: First, convert 4 cm to 40 mm.

Next, calculate = 0.3.40

12


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Converting Between Degrees and Radians


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Your Turn : Converting Between Degrees

and Radians

Convert 60to radians.

Solution: r= 60 = or 1.047.

Convert to radians.

Solution: d= = 270.

180

3

=

s

r

180

2

3


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Special Angles in the Unit Circle

We can now draw the unit circle with special

angles in degrees and radians.


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Section 3.2

Arc Length and Area of a Circular

Section

Skills Objectives Calculate the length of an

arc along a circle. Find the area of a circular

sector.

Solve application

problems involvingcircular arc lengths and

sectors.

Conceptual Objectives

Understand that to use

the arc length formula,the angle measure

must be in radians.


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Arc Length


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Find the area of a slice of pizza (cut into 8 equal pieces)

if the entire pizza has a 16-inch diameter.

Solution: r = 8, r= , so area = 25 in.2.

Calculating Area of a Circular Sector

4

2

842

1


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Linear and Angular Speed


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Your Turn: Linear Speed

A car travels at

a constant speed arounda circular track with circumference equal to3 miles. If the car records a time of 12minutes for 7 laps, what is the linear speedin miles per hour?

Solution: t = 12 minutes, or hour and

s = 7 X 3.

V = = = 105 mph.

5

1

t

s

2.

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Relationship Between Linear and

Angular Speeds


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Section 3.4

Definition 3 of Trigonometric Functions:

Unit Circle ApproachSkills Objectives

Draw the unit circle

illustrating the special

angles and label the sineand cosine values.

Determine the domain

and range of trigonometric

(circular) functions. Classify circular functions

as even or odd.

Conceptual Objectives Understand that trigonometric

functions using the unit circle

approach are consistent with both

of the previous definitions (right

triangle trigonometry and

trigonometric functions of

nonacute angles in the Cartesian

plane).

Relate x-coordinates and y-

coordinates of points on the unit

circle to the values of cosine and

sine functions.

Visualize periodic properties of

trigonometric (circular) functions.


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The Unit Circle


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Common Mistake: Using the Wrong Mode

on a Calculator

Many calculators automatically reset to degreemode after every calculation, so be sure toalways check what mode the calculatorindicates.

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Young Trig 3e Chapter3 PPT