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Trig Functions of Acute Angles

Trig Functions of Acute Angles. Lesson 2.2. A. c. b. B. C. a. Right Triangle Ratios. Given a right triangle Ratios. Right Triangle Ratios. Given a specific triangle determine the ratios How to find the hypotenuse? Use the Pythagorean theorem Ratios. 7. 5. B.

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Trig Functions of Acute Angles

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  1. Trig Functions of Acute Angles Lesson 2.2

  2. A c b B C a Right Triangle Ratios • Given a right triangle • Ratios

  3. Right Triangle Ratios • Given a specific triangledetermine the ratios • How to find the hypotenuse? • Use the Pythagorean theorem • Ratios 7 5 B

  4. Right Triangle Ratios • Note: Text suggests importance of memorizing table on pg. 137 … • Consider instead memorizing some standard triangles and deriving table as needed

  5. Right Triangle Ratios • Some important relationships for standard triangles 30° 45° 2 2 1 45° 60° 60° 1 1 1

  6. Reciprocal Trig Functions • Secant • Cosecant • Cotangent • Note: newer models of calculators will have these built in • Older systems can create functions • Older TI-89's may be updated

  7. Evaluating Trig Expressions • Use calculator • Important to keep track of when calculator is in radian or degree mode • Use 2nd D to have function evaluate with degrees, even when in radian mode

  8. Exercises for 2.2A • Page 142 • 1 – 49 EOO

  9. Solving Triangles • For now problem will involve right triangles • Usually one side and one angle will be given • Must find one or both of the other sides Distance acrossthe water? • Ask which trig ratio? • Write equation • Solve for unknown quantity 52° 31 m

  10. Solving Triangles • Some problems talk about angle of elevation • The line of sight above the horizontal • The angle of depression • The line of sight below the horizontal

  11. Solving Triangles • Ask which trig ratio? • Write equation • Solve for unknown quantity • Find the height of an object by measuring distances and the angle of elevation The angle of elevation is 37.5° 76.89 ft Experiment with Elevation Spreadsheet

  12. Exercises for 2.2B • Page 143 • Exercises53, 54, 57, 60, 63, 65,

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