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30 April 2012 Geometry Put all papers from folder in your binder.

30 April 2012 Geometry Put all papers from folder in your binder. Warm Up 1) Find x. HOMEWORK DUE TUESDAY: pg. 645: 1 – 20 FINAL PROJECT DUE MAY 8. Objective. Students will use sine, cosine and tangent ratios and their inverses to solve problems.

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30 April 2012 Geometry Put all papers from folder in your binder.

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  1. 30 April 2012 GeometryPut all papers from folder in your binder. Warm Up 1) Find x. HOMEWORK DUE TUESDAY: pg. 645: 1 – 20 FINAL PROJECT DUE MAY 8

  2. Objective Students will use sine, cosine and tangent ratios and their inverses to solve problems. Students will take notes and solve problems.

  3. Right Triangle Vocabulary hypotenuse- the longest side leg adjacent- the side that is not the hypotenuse that helps form the angle; adjacent means “next to” leg opposite- the side that does not help form the angle; side “across” the triangle ANGLE Hypotenuse Adjacent Opposite

  4. Sine, Cosine and Tangent are special ratios defined as follows:SOH CAH TOA WRITE THESE DOWN Sine = “sin” = MEMORIZE THESE!! Cosine = “cos” = Tangent = “tan” =

  5. solving equations with trig functions 1) Strategy– rewrite the trig function as a decimal and solve for the unknown value ex:  sin 42⁰ ≈ 0.6691 0.6691 = 20 (0.6691) = x x = 13. 3826

  6. solving equations with trigfunctions 2) remember sinϴ, cosϴ, tanϴ are RATIOS YOU CAN NOT DIVIDE the angle measure to simplify!!! STRATEGY– use parenthesis to help you remember! 20 (sin 42⁰) = x multiply both sides by 20 20 (0.6691) = x use calculator x = 13.2826

  7. How do you know which ratio to use? • Identify H, A and O. • What information do you have? What information do you need to find? • Use the trig ratio with “have/need” sides. DO Handout- TRIG Worksheet 3- Calculating Sides

  8. Inverse trigonometric functions UNDO trig functions: “inverse cosine”  cos-1 (cos ϴ) = ϴ “inverse sine” sin-1 (sin ϴ) = ϴ “inverse tangent”  tan-1 (tan ϴ) = ϴ As with ANY ALGEBRA- if you do it to one side, you must ALSO DO IT TO THE OTHER! If you know the RATIO of sides, you can use the INVERSE Trig functions to find the ANGLES!!

  9. example Find ϴ: First, mark H, O and A. ϴ What information do you KNOW? What trig function can you use? H 9 6 tan ϴ = O/A tan ϴ = 6/9 tan -1(tan ϴ) = tan -1 (6/9) Use inverse tangent, because you need to find the angle! ϴ = tan-1 (6/9) = 33.6901◦

  10. practice Do Trigonometry Worksheet T4 - Calculating Angles Each group will be asked to put one solution on a white board and be prepared to share their work with the class.

  11. debrief Why do the trig ratios remain equivalent for any acute angle, no matter how big the triangle? How do you know which trig function to use when solving trig problems?

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