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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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Trig equations

Trig Equations

Lesson 3.6


Find the angle for the ratio
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

1

-1

2

2


Multiple solutions
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


Multiple solutions1

Note that @n1 signifies "some arbitrary integer"

Multiple Solutions

  • Other solution methods

  • This gives us our multiple solutions


Multiple solutions2
Multiple Solutions

  • Also possible to limit the domain of the answers

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


Using inverse functions
Using Inverse Functions

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


Quadratic trig equations
Quadratic Trig Equations

  • Usually they will factor

Also possible to use the quadratic formula


Assignment
Assignment

  • Lesson 3.6 – Assignment Part A

  • Page 278

  • Exercises 1 – 59 EOO


Solving angle of inclination
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


Modeling sinusoidal data
Modeling Sinusoidal Data

Choo

  • Note sunset time for selected days of the year

  • Enter intodata matrix

  • Graph (zoomdata)

  • Use sin regression


Assignment1
Assignment

  • Lesson 3.6 Part B

  • Page 279

  • Exercises 85-97 odd


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