1. 4.3 - R IGHT T RIANGLE T RIGONOMETRY

2. I N THIS SECTION, YOU WILL LEARN TO :  Evaluate trigonometric functions of acute angles  Use fundamental trigonometric identities  Use a calculator to evaluate trigonometric functions

3. S IX T RIGONOMETRIC F UNCTIONS OF A R IGHT T RIANGLE :  Use SOH CAH TOA to remember all six of the trigonometric functions:

4. E XAMPLE : 12

5. A NSWERS : Use the Pythagorean Theorem to find the hypotenuse: 6 12

6. S PECIAL R IGHT T RIANGLES :

7. S IX TRIGONOMETRIC VALUES OF THE SPECIAL RIGHT TRIANGLES : * Note that certain sine and cosine angles are equal.

8. C OFUNCTIONS OF COMPLEMENTARY ANGLES ARE CONGRUENT : Sine-Cosine, Tangent-Cotangent, and Secant-Cosecant are cofunctions.

9. E XAMPLE OF COMPLEMENTARY ANGLES : Use the given function values and the cofunction relationships to find the indicated trigonometric functions.

10. ANSWERS:

11. F UNDAMENTAL T RIGONOMETRIC I DENTITIES : A) Reciprocal Identities :

12. F UNDAMENTAL T RIGONOMETRIC I DENTITIES : B) Quotient Identities:

13. F UNDAMENTAL T RIGONOMETRIC I DENTITIES : C) Pythagorean Identities:

14. P ROOF OF THE S INE P YTHAGOREAN I DENTITY : Prove:

15. E XAMPLES :

16. A NSWERS :

17. E XAMPLES : 2) Use trigonometric identities to transform the left side of the equation into the right side.

18. A NSWERS :

19. C ALCULATOR E XAMPLES :

20. A NSWERS : :

21. C ALCULATOR E XAMPLES :

22. A NSWERS :