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 found Graphically Using Reference Angle

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 -1 x … …

4 Multiple Solutions  Other solution methods  This gives us our multiple solutions Note signifies "some arbitrary integer"

5 Using Inverse Functions  We can take the inverse cosine of both sides to solve the function

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

7 Assignment  Lesson 3.6 – Assignment Part A  Page 232  Exercises 1 – 59 EOO

8 Solving Angle of Inclination  Note the Excel spreadsheet, PumpkinElevation.xls PumpkinElevation.xls Use for problem 92, pg 233  It uses the formula  Given a distance, we solve for θ

9 Modeling Sinusoidal Data  Note sunset time for selected days of the year  Enter into data matrix  Graph (zoom data)  Use sin regression DateDay of YearSunset Time Jan 1117:03 Feb 13217:39 Mar 16018:15 Apr 19118:51 May :25 Jun :56 Jul :07 Aug :46 Sep :00 Oct :08 Nov :19 Dec :54

10 Assignment  Lesson 3.6 Part B  Page 233  Exercises odd