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Trig Equations

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Trig Equations

Lesson 3.6

- 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

1

-1

2

2

- 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

…

…

Note that @n1 signifies "some arbitrary integer"

- Other solution methods
- This gives us our multiple solutions

- Also possible to limit the domain of the answers
- Then you don't get a representation of all possible answers

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

- Usually they will factor

Also possible to use the quadratic formula

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

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

- It uses the formula
- Given a distance, we solve for θ

Choo

- Note sunset time for selected days of the year
- Enter intodata matrix
- Graph (zoomdata)
- Use sin regression

- Lesson 3.6 Part B
- Page 279
- Exercises 85-97 odd