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Trig Equations

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

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  1. 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 1 -1 2 2

  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 … …

  4. Note that @n1 signifies "some arbitrary integer" Multiple Solutions • Other solution methods • This gives us our multiple solutions

  5. Multiple Solutions • Also possible to limit the domain of the answers • Then you don't get a representation of all possible answers

  6. Using Inverse Functions • We can take the inverse cosine of both sides to solve the function

  7. Quadratic Trig Equations • Usually they will factor 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

  10. Modeling Sinusoidal Data Choo • Note sunset time for selected days of the year • Enter intodata matrix • Graph (zoomdata) • Use sin regression

  11. Assignment • Lesson 3.6 Part B • Page 279 • Exercises 85-97 odd

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