1. 1 7.3 Evaluating Trig Functions of Acute Angles In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles Using trigonometry to solve right triangles

2. 2 The 45º- 45º- 90º Triangle Special Right Triangles 1 1 45º Find the exact values of the six trig functions for 45  sin 45° =csc 45° = cos 45° =sec 45° = tan 45° =cot 45° = Ratio of the sides: MEMORIZE! I AM A VERY IMPORTANT SLIDE!

3. 3 The 30º- 60º- 90º Triangle Find the exact values of the six trig functions for 30  sin 30  =csc 30  = cos 30  =sec 30  = tan 30  =cot 30  = 1 60º 30º 2 Ratio of the sides: MEMORIZE! Special Right Triangles I AM A VERY IMPORTANT SLIDE, TOO!

4. 4 The 30º- 60º- 90º Triangle Find the exact values of the six trig functions for 60  sin 60  =csc 60  = cos 60  =sec 60  = tan 60  =cot 60  = 1 60º 30º 2 Ratio of the sides: MEMORIZE! Special Right Triangles DON’T FORGET ABOUT ME!

6. 6 To evaluate trig functions of acute angles other than 30 , 45 , and 60 , you will use the calculator. Your calculator has keys marked   . **Make sure the MODE is set to the correct unit of angle measure. (Degree vs. Radian) Example: Find to two decimal places. Using the calculator to evaluate trig functions

7. 7 To find the values of the remaining three functions (cosecant, secant, and tangent), use the reciprocal identities. WARNING: DO NOT USE THE INVERSE FUNCTIONS; e.g. SIN -1 Example: (Give answers to three decimal places) 1. Find 2. Find Using the calculator to evaluate trig functions

8. 8 When you are given two sides of a right triangle and you want to find the angle OR when you are given one side and one acute angle and you want to find one of the remaining sides, you will use a process called solving right triangles. PLAN Sketch a right triangle and label the angle and/or side(s) given Use the definitions of the six trig functions to determine which function is appropriate to use. If you have angles of 30º, 60º, or 45º, use the special reference triangles (ratios of the sides) to solve the triangle. Otherwise, use your calculator to evaluate the trig function. Solving a right triangle

9. 9 Example Solve the triangle. Solving a right triangle Solution: 52º 9.6 Reminder: Make sure your MODE is set to “Degree”

15. 15  End of Section 7.3