Section 7-4 Evaluating and Graphing Sine and Cosine Objective: Day 1: Reference angles. Day 2: Parent Graphs of sine and cosine function Day 3: UC and parent graphs; application problems.

DU/UNIT/UNIT.HTM The curve bank!

The site below demonstrates 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

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

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

Sec 7.4 Day 2 Review: express each in terms of the reference angle: 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: RadiansDegreesNotes The Period The amplitude The coordinates of the starting point aka Y-intercept aka The maximum First x intercept The minimum point Second x intercept End point

Parent graph: cosine function

Critical values of the parent graph of the sine function: RadiansDegreesNotes The Period The amplitude The coordinates of the starting point aka Y-intercept aka The maximum First x intercept The minimum point Second x intercept End point

Parent graph: sine function

All at once! 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!

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 7.4 Part 1: #1-17 odds #21-24 ALL Use your 4-day weekend wisely. Part 2: #26-31 All