The Pythagorean Theorem

1. The Pythagorean Theorem From The Simpson’s Homer copies the Scarecrow on The Wizard of Oz.

2. The Pythagorean Theorem The sum of the square of the two sides of a right triangle is equal to the square of the hypotenuse.

3. The sum of the square of the two sides of a right triangle is equal to the square of the hypotenuse.

4. r 12 10 An example of the Pythagorean Theorem • Let the adjacent side of the right triangle be 10 and the opposite side be 12. Find the hypotenuse of the right triangle.

5. 13 y 12 Now you try it! • Let the adjacent side of the right triangle be 12 and the hypotenuse be 13. Find the opposite side of the right triangle.

6. Definition of the Trig. Functions

7. r 12 10 An example of the Trigonometric Functions • Let the adjacent side of the right triangle be 10 and the opposite side be 12. Find all the trigonometric functions of the given angle theta.

8. 12 10

9. 13 y 12 Now you try it! • Let the adjacent side of the right triangle be 12 and the hypotenuse be 13. Find all the trigonometric functions of the given angle theta.

10. 13 5 12

11. 30° 2 2 y 60° 1 Special Angles and Trig. Functions • The 30°-60°-90° triangle: Thus the 30°-60°-90° triangle sides are in the ratio of 1 - - 2.

12. 30° 2 2 60° 1 Trig. Functions of 30°-60°-90° triangles.

13. r 45° 1 45° 1 Special Angles and Trig. Functions • The 45°-45°-90° triangle: Thus the 45°-45°-90° triangle sides are in the ratio of 1 - 1 - .

14. 45° 1 45° 1 Trig. Functions of 45°-45°-90° triangles.

15. The Unit Circle

16. The Unit Circle: