1. Trig Equations Lesson 3.6

2. 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 1 2222

3. 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. 4 Multiple Solutions  Other solution methods  This gives us our multiple solutions Note that @n1 signifies "some arbitrary integer"

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

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

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

8. 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. 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 112119:25 Jun 115219:56 Jul 118220:07 Aug 121319:46 Sep 124419:00 Oct 127418:08 Nov 130517:19 Dec 133516:54

10. 10 Assignment  Lesson 3.6 Part B  Page 233  Exercises 85-99 odd