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

3. 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 .

4. Trigonometric Functions • 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: • Sine • Cosine • Tangent • Cosecant • Secant • Cotangent

5. Six Trigonometric Functions

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

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

9.  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.

10.  5 9 Example (cont) So the six trig functions are:

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

14. This is known as a Pythagorean Identity.

15. Divide each side by cos2 x to derive 2nd Pythagorean Identity.

16. Divide each side by sin2 x to derive 3rd Pythagorean Identity.

23. End of Section 7.2