Trig Equations

Lesson 3.6

2

Find the Angle for the Ratio

Given the equation

We seek the angle (the value of x) for which the cosine gives the ratio

Answer can be foundGraphically Using Reference Angle

3cos

2x

3 / 2

1

-1

2

2

3

6

11

6

3

Multiple Solutions

Note that many solutions often exist

Often we restrict the solution to the range of the inverse functions (see page 214) The range of

cos-1x

……

0 y

4

Multiple Solutions

Other solution methods

This gives us our multiple solutions

Note that @n1 signifies "some

arbitrary integer"

Note that @n1 signifies "some

arbitrary integer"

112 2

6 6k or k

Multiple Solutions

Also possible to limit the domain of the answers

Then you don't get a representation of all possible answers

5

6

Using Inverse Functions

We can take the inverse cosine of both sides to solve the function

1 1

3cos

2

3cos cos cos

2

x

x

x

11

2 26 6

k or k

7

Quadratic Trig Equations

Usually they will factor

24cot 3cot 0x x 22sin 5sin 3 0x x

tan sin sin 0x x x

22cos 5cos 5 0x x

Also possible to use the quadratic formula

Also possible to use the quadratic formula

8

Assignment

Lesson 3.6 – Assignment Part A Page 278 Exercises 1 – 59 EOO

9

Solving Angle of Inclination

Note the Excel spreadsheet, PumpkinElevation.xls Use for problem 92, pg 267

It uses the formula

Given a distance, we solve for θ

2_sin cos

16

initial velocitydist

10

Modeling Sinusoidal Data

Note sunset time for selected days of the year

Enter intodata matrix

Graph (zoomdata)

Use sin regression

Date Day of Year Sunset Time

Jan 1 1 17:03

Feb 1 32 17:39

Mar 1 60 18:15

Apr 1 91 18:51

May 1 121 19:25

Jun 1 152 19:56

Jul 1 182 20:07

Aug 1 213 19:46

Sep 1 244 19:00

Oct 1 274 18:08

Nov 1 305 17:19

Dec 1 335 16:54

11

Assignment

Lesson 3.6 Part B Page 279 Exercises 85-97 odd