1. 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. 2 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 . The sides of a right triangle  Side adjacent to  Side opposite  Hypotenuse 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. 3 Six Trigonometric Functions

4. 4

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

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

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

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

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

12. This is known as a Pythagorean Identity.

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

14. 14 Divide each side by sin 2  to derive 3 rd Pythagorean Identity.

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21. 21 End of Section 7.2