1. Quiz 13-2 1. 2. 3. Convert to degrees Convert to radians Arc length = Arc length = inches Radius = Radius = 6 inches What is the angle measure (in radians)?

2. 13-1 Trigonometric Functions of Acute Angles

3. What you’ll learn about Right Triangle Trigonometry Two Famous Triangles Evaluating Trigonometric Functions with a Calculator Applications of Right Triangle Trigonometry … and why The many applications of right triangle trigonometry gave the subject its name.

4. Right Triangle Review What is the measure of this angle? 90º What measure do these two angles add up to? two angles add up to? A B C

5. Right Triangle Review What are these two side of the triangle called? of the triangle called? What is the name of this side of the triangle? side of the triangle? A B C hypotenuse legs

6. Right Triangle Review The Pythagorean Theorem relates the lengths of the two legs to the hypotenuse. What is the of the two legs to the hypotenuse. What is the equation of this relation? equation of this relation? a b c

7. Right Triangle Review If: a = 3 b = 4 Then: c = ? a b c 3 4 (formula problem) c = 5

8. Right Triangle Review If: c = 7 b = 4 Then: a = ? a b c10 4 (formula problem)

9. Your turn: 1. a b c c = ? 2. a = ?

10. Trigonometric Functions SOHCAHTOA “Some old horse caught another horse caught another horse taking oats away.” Key point: sine of an angle (measured in degrees or radians) These only work for right triangles!!!

11. Sine Ratio 3 x 5 A B C What is the sine ratio for angle A? ratio for angle A? opp Sine ratio for angle A is Sine ratio for angle B = ? Sine ratio for angle B =

12. Your Turn: 8 x 17 A B C 3. What is the sine ratio for angle A? 4. What is the sine ratio for angle B?

13. Cosine Ratio 3 4 5 A B C What is the cosine ratio for angle A? ratio for angle A? adj Cosine ratio for angle A is

14. Your Turn: 8 15 17 A B C 3. What is the cosine ratio for angle A? 4. What is the cosine ratio for angle B?

15. Tangent Ratio 3 4 5 A B C What is the tangent ratio for angle A? ratio for angle A? adj Tangent ratio for angle A is opp

16. Your Turn: 8 15 17 A B C 5. What is the tangent ratio for angle A? 6. What is the tangent ratio for angle B?

17. Evaluating Trig. Functions of 45 º 45º x x = ? x = 45º A C B If AB = 45º AC = ? BC = ??

18. Your Turn: Find all 3 trigonometric ratios of a 45º – 45º – 90º triangle. 45º A C B 1 7. 8. 9.

19. What if the triangle is still 45-45-90 BUT is bigger? Find: sin 45º Sin 45º does not change regardless of the size of the 45-45-90 triangle!!! of the size of the 45-45-90 triangle!!! Rationalize the denominator Which one is easier to calculate: (1) hypotenuse = (1) hypotenuse = (2) hypotenuse = (2) hypotenuse = 1

20. That’s why we use the UNIT CIRCLE, the hypotenuse of the triangle is always ‘1’. r = 1 45º Find: sin 45º = Let’s put the triangle on top of the unit circle. on top of the unit circle. 45º

21. Trig. Functions of the 30º-60º-90º triangle 30º A C B 2 60º 1 3 A C B 1 ½ Shrink by ½ 30º 60º ½ ½ 8. 9. Your Turn:

22. Use your calculator to find trig ratios Sin 30º = ? Make sure it’s in degree mode. Sin 30º = 0.5 Sin 60º = ? ½ ½ Sin 60º = Sin 60º = 0.8660

23. Relate back to the UNIT CIRCLE r = 1 Find: sin 60º Using the unit circle: Using the upper right triangle: 30º A C 60º B 30º ACB 2 60º 1 3

24. Solving a Right Triangle: Find the measure of every other angle and side. A right triangle has a hypotenuse that is 5 inches long. One of the acute angles is 43º. inches long. One of the acute angles is 43º. 43º ACB 1.Draw the picture with the given information. the given information. 2. Pick the “low hanging fruit” (do the easy parts) fruit” (do the easy parts) 57º 5 3. Use trig ratios to solve for the unknown side lengths. x y sin 43º = y/5 y = 5 sin 43º = 3.4 3.4 cos 43º = x/5 x = 5 cos 43º = 3.7

25. Your Turn: 25º ACB 10. 11. 12. 2 AB = ? BC = ?

26. Vocabulary Angle of elevation: angle above horizon. Horizontal line Angle of depression: angle below horizon. Horizontal line

27. HOMEWORK Section 13-1 (page 856) (evens) (3 trig functions not 6) 4 (3 pts), 10 (2 pts), 18-20, (1 pt each), 22-28 (3 pts each), 32 (2 pts) Review: 44 (1 pt) (25 points)