7.2 Right Triangle Trigonometry

1. 7.2 Right Triangle Trigonometry In this section, we will study the following topics: Evaluating trig functions of acute angles using right triangles Use Fundamental Identities Use the Complimentary Angle Theorem

2. Hypotenuse Side opposite  Side adjacent to  The sides of a right triangle Take a look at the right triangle, with an acute angle, , in the figure below. Notice how the three sides are labeled in reference to . We will be reviewing special ratios of these sides of the right triangle, with respect to angle, . These ratios are better known as our six basic trig functions.

3. Six Trigonometric Functions

5. Definitions of the Six Trigonometric Functions To remember the definitions of Sine, Cosine and Tangent, we use the acronym : “SOHCAHTOA”

6. Find the value of each of the six trigonometric functions of the angle .

7.  5 9 Example Find the exact value of the six trig functions of : Hint: First find the length of the hypotenuse using the Pythagorean Theorem.

8.  5 9 Example (cont) So the six trig functions are:

9. Example Given that  is an acute angle and , find the exactvalue of the six trig functions of .

12. This is known as a Pythagorean Identity.

13. Divide each side by cos2 to derive 2nd Pythagorean Identity.

14. Divide each side by sin2 to derive 3rd Pythagorean Identity.

21. End of Section 7.2