1 Trig Functions of Acute Angles Lesson 2.2

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

3 Right Triangle Ratios  Given a specific triangle determine 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 60° 30° ° 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 2 nd 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 52° 31 m Distance across the water? Ask which trig ratio? Write equation Solve for unknown quantity Ask which trig ratio? Write equation Solve for unknown quantity

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

12 Exercises for 2.2B  Page 143  Exercises 53, 54, 57, 60, 63, 65,