Section 7-4 Evaluating and Graphing Sine and Cosine

Objective:Day 1: Reference angles.Day 2: Parent Graphs of sine and cosine functionDay 3: UC and parent graphs; application problems.

HTTP://CURVEBANK.CALSTATELA.EDU/UNIT/UNIT.HTM

The curve bank!

The site below demonstrates reference angles.

• Reference Angles

Reference Angles

• The angle = 20° is called the reference angle for the 160°angle. It is also the reference angle for the 200° and 340° angles.

Reference Angles

• In general, the acute angle is the reference angle for the angles:

• as well as all coterminal angles. In other words, the reference angle for any angle θ is the acute positive angle formed by the terminal ray of θ and the x-axis.

Remember:  The reference angle is measured from the terminal side of the original angle "to" the x-axis (not the y-axis).

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

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α180º-α

180º+α 360º-α

Degrees

π-α

π+α 2π-α

radianREFERNCE ANGLES

Example

• Express sin 695° in terms of a reference angle.

Sec 7.4 Day 2

• Review: express each in terms of the reference angle:

3

2cos

4

3sin

cos -123 °

sin 473°

Graphing sine and cosine functions

Graphing using your calculator. • When angle measure is in degrees or in

radians.

Graphing without your calculator.• When angle measure is in degrees or in radians.

Critical values of the parent graph of the cosine function:

Radians Degrees Notes

The Period

The amplitude

The coordinates of the starting pointaka Y-intercept aka The maximumFirst x intercept

The minimum point

Second x intercept

End point

Parent graph: cosine function

x

y

-1

1

0

Critical values of the parent graph of the sine function:

Radians Degrees Notes

The Period

The amplitude

The coordinates of the starting pointaka Y-intercept aka The maximumFirst x intercept

The minimum point

Second x intercept

End point

Parent graph: sine function

x

y

-1

0

1

All at once!

x

y

-1

0

1

What do you think: a) The

coordinates of the intersection point are?

b) Where would you find the intersection points on the UC?

All at once but more than once!

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y

-1

0

1

SIMULATION OF SINE AND COSINE GRAPHS

See the site below for cool demonstartion

How to use your calculator to find sin and cos

• Before doing any calculations involving trig functions always check the calculator mode.

Make sure to check the mode then evaluate the expressions below:

• Find the value of each expression to three decimal places.

• A.) sin 122°• B.) cos 237°• C.) cos 5 • D.) sin (-2)

Latitude

• The latitude of a point on Earth is the degree measure of the shortest arc from that point to the equator. For example, the latitude of point P in the diagram equals the degree measure of arc PE.

How far is Rome (aka Roma) from the equator?

• The Latitude of Rome is approximately 42 N.

The radius of earth is approximately 3963 miles

Remember s=r where is measured in radians.

How far is Santiago, Chile from the equator?

•The latitude of Santiago is 33º 28´ S.

Homework written exercises sec 7.4Part 1:#1-17 odds#21-24 ALL• Use your 4-day weekend wisely.

Part 2: #26-31 All