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Trig Equations - PowerPoint PPT Presentation

Trig Equations. Lesson 3.6. 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 found Graphically Using Reference Angle. 1 -1. 2 2. Multiple Solutions.

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Presentation Transcript

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

Multiple Solutions

• 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