1. Geometry Trig Lesson Test 2 Algebra 2 textbook, Prentice Hall, p.792

2. Understand and use trigonometric relationships of acute angles in triangles. Determine side lengths of right triangles by using trigonometric functions. Objectives

3. *Sin, Cos, Tan *Sin -1, Cos -1, Tan -1 I can solve…

4. Teaching slide Example 1: Finding Trigonometric Functions Find the values of the three (there are actually six) trigonometric functions for θ. Step 1 Find the length of the hypotenuse. 70 24 θ a 2 + b 2 = c 2 c 2 = 24 2 + 70 2 c 2 = 5476 c = 74 Pythagorean Theorem. Substitute 24 for a and 70 for b. Simplify. Solve for c. Eliminate the negative solution.

5. Example 1: Finding Trigonometric Functions Find the values of the three (there are actually six) trigonometric functions for θ. Step 1 Find the length of the hypotenuse. 70 24 θ a 2 + b 2 = c 2 Pythagorean Theorem.

6. Example 1 answers Step 2 Find the function values.

7. In each reciprocal pair of trigonometric functions, there is exactly one “co” Helpful Hint Teaching note

8. SIX trigonometric function sine cosine tangent cosecants secant cotangent Vocabulary

9. Find the values of the six trigonometric functions for θ. Step 1 Find the length of the hypotenuse. 80 18 θ a 2 + b 2 = c 2 c 2 = 18 2 + 80 2 c 2 = 6724 c = 82 Pythagorean Theorem. Substitute 18 for a and 80 for b. Simplify. Solve for c. Eliminate the negative solution. Teaching note Example 2

10. Find the values of the six trigonometric functions for θ. Step 1 Find the length of the hypotenuse. 80 18 θ a 2 + b 2 = c 2 Pythagorean Theorem. Example 2

11. Example 2 answers Step 2 Find the function values.

12. Teaching note Example 3: Finding All Trigonometric Functions Find the values of the six trigonometric functions for θ. Step 1 Find the length of the hypotenuse. 70 24 θ a 2 + b 2 = c 2 c 2 = 24 2 + 70 2 c 2 = 5476 c = 74 Pythagorean Theorem. Substitute 24 for a and 70 for b. Simplify. Solve for c. Eliminate the negative solution.

13. Example 3: Finding All Trigonometric Functions Find the values of the six trigonometric functions for θ. Step 1 Find the length of the hypotenuse. 70 24 θ a 2 + b 2 = c 2 Pythagorean Theorem.

14. Example 3 answers Step 2 Find the function values.

15. Application Assignment Due next class; Copy on your own paper; in chart form (see below) TRI IDRatioInverse Trig ID Ratio sin Acsc A cos ASec A tan Acot A sin Bcsc B cos B tan Bcot B B A C Info: AB = 25 CA = 16 CB = 9

16. I can solve for… Technology with trig functions

17. Make sure that your graphing calculator is set to interpret angle values as degrees. Press. Check that Degree and not Radian is highlighted in the third row. Caution! Clear calculators first ALWAYS

18. Steps: 2 nd  +  712  enter  clear MODE  using arrow keys twice down and once over right  enter  2 nd  MODE.

19. Example 4-2a Use a calculator to find tan to the nearest ten thousandth. KEYSTROKES: 56 1.482560969 TAN ENTER Answer: Example 1

20. Example 2: Calculating Trigonometric Ratios Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° sin 52°  0.79 Be sure your calculator is in degree mode, not radian mode. Caution!

21. Example 3 Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. cos 30° cos 30°  0.87

22. Example 4 Use your calculator to find each angle measure to the nearest degree. a. tan -1 (0.71)b. cos -1 (0.05)c. sin -1 (0.67) cos -1 (0.05)  87°sin -1 (0.67)  42°tan -1 (0.75)  35°

23. I can solve… *Given degree and one side, solve for “ ? “ ?? given

24. note taking skills Step Example of step one piece of paper

25. Ex. 1: Finding Side Lengths of Right Triangles Use a trigonometric function to find the value of x. steps What do I know from image, what do I need ? opposite and hypotenuse OPPOSITEOPPOSITE HYPOTEHYPOTE What trig function contains OPPOSITE and HYPOTENUSE ? sin = opp hyp Fill in knowns and unknown, rearrange to solve for unknown sin 30 = X 74

26. sin 30 = X 74 Example 1 cont. 74 the term I am solving for is isolated, HEY! Calculator: 74  sin  30  enter X = 37

27. EX. 2 Use a trigonometric function to find the value of x. Steps: 1)What do I know ? 2)What trig function contains opposite and hypotenuse? 3)Fill in knowns and unknowns 4)Isolate what we are solving for 5)calculator Example of step: 1)Hypotenuse & Opposite 2)Sine = opp hyp 3) Sin 45 = X 20 4) 20 sin 45 5) 14.14

28. Teaching note Ex. 3 A surveyor whose eye level is 6 ft above the ground measures the angle of elevation to the top of the highest hill on a roller coaster to be 60.7°. If the surveyor is standing 120 ft from the hill ’ s base, what is the height of the hill to the nearest foot? Step 1 Draw and label a diagram to represent the information given in the problem. 120 ft 60.7° Previous slide, only one slide for students; blank work area follows

29. Teaching note Ex. 3 Cont. Use the tangent function. 120(tan 60.7°) = x Substitute 60.7 for θ, x for opp., and 120 for adj. Multiply both sides by 120. Step 2 Let x represent the height of the hill compared with the surveyor ’ s eye level. Determine the value of x. 214 ≈ x Use a calculator to solve for x. **students NOT done yet, have them look at problem again, they will forget to include the 6 ft.** 214 + 6 = 220.

30. Teaching note Ex. 3 Cont. Step 3 Determine the overall height of the roller coaster hill. x + 6 = 214 + 6 = 220 The height of the hill is about 220 ft.

31. Ex. 3 A surveyor whose eye level is 6 ft above the ground measures the angle of elevation to the top of the highest hill on a roller coaster to be 60.7°. If the surveyor is standing 120 ft from the hill ’ s base, what is the height of the hill to the nearest foot?

33. Teaching note Ex. 4: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. BC? is adjacent to the given angle,  B. You are given AC, which is opposite  B. Since the adjacent and opposite legs are involved, use a tangent ratio.

34. Example 4 Continued BC  38.07 ft Write a trigonometric ratio. Substitute the given values. Multiply both sides by BC and divide by tan 15°. Simplify the expression.

35. Ex. 4: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. BC?

36. ***I can solve… Given two sides, solve for degree (inverse????) given ??

37. ***I can solve… Two degrees and one side give; solve for other side given ????