Solving Trigonometric Equations: Find Angle for Ratio

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 foundGraphically Using Reference Angle 1 -1 2 2

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 … …

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

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

Quadratic Trig Equations • Usually they will factor Also possible to use the quadratic formula

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

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

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

Solving Trigonometric Equations: Find Angle for Ratio