Chapter 10 - NCPN

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Activity 2: The Sun Today Problem Statement Use a protractor to approximate the angle of the sun at different times during the day. Model the position of the sun in the sky with a graph. Then use your graph to predict the position of the sun in the sky at different times during the day. Equipment Clock Grid paper Level Protractor Yard sticks Procedure 1 Work with a partner. At various times throughout the day (on a sunny day) go outside and use the yard sticks, level, and protractor to measure the angle of the sun with respect to a level horizon. Have your partner hold a yard stick level in the direction of the sunrise. Form an angle by pointing the other yard stick directly at the center of the sun. Hold the yard sticks as steady as possible and use the protractor to measure the angle. 2 Collect data at various times during the day to complete a table such as the one shown below. see margin 3 Use your protractor to draw a large semicircle on grid paper. Place markings along the semicircle at every 30° like the one shown at the left. Draw each angle from your data on the semicircle and label each corresponding time. see margin Time of Day 9:00 A.M. 10:00 A.M. 11:00 A.M. 12:00 Noon 1:00 P.M. 2:00 P.M. 3:00 P.M. Angle of the Sun 4 What was the change in the angle of the sun between 9:00 A.M. and 10:00 A.M. Use your data and your graph to predict the position of the sun at 9:30 A.M. sample answer: 15°, about 52.5° off the Eastern horizon 5 What was the change in the angle of the sun between noon and 1:00 P.M. Use your data to predict the position of the sun at 12:30 P.M. sample answer: 15°, about 97.5° off the Eastern horizon 6 How do you think your data would change if it were gathered at different times during the year Answers will vary. 492 Chapter 10 Trigonometric Functions and Identities
Activity 3: The Sine Curve of Biorhythms Some believe that a person’s physical, emotional, and intellectual well-being are based on cycles that model sine curves. This unscientific theory is based on the idea that these three cycles begin on the day one is born and throughout one’s life the three cycles have high points and low points that occasionally coincide. Problem Statement Use the Internet to locate and print a biorhythm chart based on your date of birth. Translate each of your biorhythm sine curve graphs into an equation. The equation of a sine curve is given by y – k = Asin B(x – h) where k is the vertical offset, h is the horizontal offset, A is the amplitude and B is the period. Follow the steps to transform a sine curve graph to an equation. Equipment Computer with Internet access and a printer Steps to Transform a Sine Curve to an Equation 1. Find the minimum and maximum point on the y-axis and calculate the amplitude A. 2. Find the period B by using the equation period length = 2≠ B where B is the period of the sine curve. 3. Find the first “zero” point. This is the first point where the horizontal line midway between the minimum and maximum y values intersects the sine curve. Use this point to calculate k and h. Procedure 1 Locate a website on the Internet where you can generate a personalized biorhythm chart. Print a copy of the graphs. A sample chart is shown on the next page. 2 Find the minimum and maximum values of the Intellectual sine curve on the y-axis and calculate the amplitude. sample answer: A = 100 3 Find the period of the Intellectual sine curve. sample answer: B = 2 29 4 Estimate the “zero” point and use this coordinate to determine the values of h and k. Sample answer: h = 7, k = 0 π Math Labs 493
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Chapter 10 Contents 10.1 Right Tria
Page 3 and 4:
Lesson 10.1 Right Triangle Trigonom
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Solution Use the definitions of the
Page 7 and 8:
Solve for x in each right triangle.
Page 9 and 10: 30. A wheelchair ramp is 20 feet lo
Page 11 and 12: Arc Length The unit circle has a ra
Page 13 and 14: Using a Calculator A scientific cal
Page 15 and 16: Find the length of the intercepted
Page 17 and 18: Lesson 10.3 Inverse Trigonometric F
Page 19 and 20: see margin After taking off, a comm
Page 21 and 22: 20. What is the angle of descent of
Page 23 and 24: The y-values on the unit circle are
Page 25 and 26: Example 2 Graphing Cosine Functions
Page 27 and 28: Activity Using a Graphing Calculato
Page 29 and 30: 25. The function y = 3sin ≠ t mod
Page 31 and 32: Ongoing Assessment In PQR, m∠P =
Page 33 and 34: Activity Ambiguous Cases Two triang
Page 35 and 36: Lesson Assessment Think and Discuss
Page 37 and 38: 23. Two points in a forest, A and B
Page 39 and 40: Lesson 10.6 Verifying Trigonometric
Page 41 and 42: Activity 2 Using the Pythagorean Id
Page 43 and 44: Lesson 10.7 Angle Sum and Differenc
Page 45 and 46: Practice and Problem Solving Use a
Page 47 and 48: Lesson 13.4 Double-Angle and Half-A
Page 49 and 50: When Trigonometric Function Values
Page 51 and 52: Practice and Problem Solving Use a
Page 53 and 54: Lesson 10.9 Solving Trigonometric E
Page 55 and 56: Use the Zero-Product Property to se
Page 57 and 58: Practice and Problem Solving Solve
Page 59: Math Labs Activity 1: The Circle of
Page 63 and 64: 3 Hold a protractor upside down so
Page 65 and 66: 3 Cale, Tammie, and Allison are mem
Page 67 and 68: 8 Bella does freelance marketing wo
Page 69 and 70: Health Occupations 13 Dmitri wants
Page 71 and 72: Lessons 10.5 and 10.6 Review Exampl
Page 73: Standardized Test Practice Multiple
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Chapter 10 - NCPN

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