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7.3 Evaluating Trig Functions of Acute Angles

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. 45 º. 1. 45 º. 1. I AM A VERY IMPORTANT SLIDE!. Special Right Triangles.

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7.3 Evaluating Trig Functions of Acute Angles

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

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

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

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

  6. Using the calculator to evaluate trig functions 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. Find2. Find

  7. Solving a right triangle • 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.

  8. 52º 9.6 Solving a right triangle Example Solve the triangle. Solution: Reminder: Make sure your MODE is set to “Degree”

  9. End of Section 7.3

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