Trig Functions of Acute Angles Lesson 2 2

Trig Functions of Acute Angles Lesson 2. 2 1

Right Triangle Ratios ¡ Given a right triangle A b C ¡ Ratios c B a View Excel Demo 2

Right Triangle Ratios Given a specific triangle determine the ratios ¡ How to find the hypotenuse? ¡ l ¡ Use the Pythagorean theorem 7 5 B Ratios 3

Right Triangle Ratios • Note: Text suggests importance of memorizing table on pg. 114 … • Consider instead memorizing some standard triangles and deriving table as needed 4

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

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

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 ¡ 7

Exercises for 2. 2 A ¡ Page 142 ¡ 1 – 49 EOO 8

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

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

Solving Triangles • Ask which trig ratio? • Write equation ¡ Find the height of an object • Solve by for unknown quantity measuring distances and the angle of elevation The angle of elevation is 37. 5° 76. 89 ft Experiment with Elevation Spreadsheet 11

Exercises for 2. 2 B Page 143 ¡ Exercises 53, 54, 57, 60, 63, 65, ¡ 12