Warm Up

8-1 Simple Trigonometric Equations Objective: To solve simple Trigonometric Equations and apply them

Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 3 x y π π 6 -7 π 6 π 6 5 π 6 13 π 6 17 π 6 25 π 6 -π-π -2 π -3 π π 2π2π 3π3π 4π4π All the solutions for x can be expressed in the form of a general solution. y = y=sin x

Solving for angles that are not on UC We will work through solutions algebraically and graphically. Learning both methods will enhance your understanding of the work.

Method 1: Algebraically: Step 1 Set the calculator in degree mode and use the inverse sine key

Find the final answer(s) for the given range. Since the answer given by your calculator is NOT between 0 and 360 degrees, find the proper answers by using RA.

Solving Graphically

Method 1: Algebraically: Step 1 Set the calculator in radian mode and use the inverse sine key

Step 2: Determine the proper quadrant

Method 2: Graphically: Step 1 Set the calculator in radian mode.

Use your Knowledge of trig functions to choose an appropriate window Use the intersect Key once more for the second point of intersection. i.e solution.

When you use the graphing method, you can easily see there is more than one solution. When using the graphing method, it might take a while to set the window properly. The algebraic method is quicker, however, you have make sure to look for a possible second answer.

To solve an equation involving a single trigonometric function, we first transform the equation so that the function is alone on one side of the equals sign. Then we follow the same procedure used in Example 1.

Example 2

Find the appropriate quadrant

Another way; ignore the negative sign.

Graphing Calculator: Although this is a reasonable window to start with, it does not capture the graph. So change Ymin and Ymax.

Warm Up Day 2; Graph sine, cosine and tangent functions.

Inclination and Slope

Theorem

Homework: Sec 8.1 Written exercises #1-21 odds Optional: Sec 8.2 written exercises ALL