Unit 7 Trigonometry Project Name Key Project Information

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1 Unit 7 Trigonometry Project Name Key Project Information What is it? This project will be a series of tasks that you must complete on your own. Specific instructions are given for each task, but all must be complete and on time for full credit When is it due? The due date is Sunday 5/21/2017 by no later than 11:59:59 PM. Since the project is submitted electronically, you can turn it in at any point you are finished. Read the How do I submit my project? section to see details on what to do after all tasks are finished. 25 points of the project are just for submitting it on time and you automatically lose 25 points after it is late! How is it graded? A specific rubric is given below. All assignments are graded on accuracy and completeness, not just effort. Come to SMART lunch if you are having issues with the project. Project Rubric: 25 points: Project is submitted electronically by 11:59:59 PM on Sunday 5/21/2017. No excuses for later submissions will be accepted; you automatically lose 25 points for failure to submit by the deadline. To make sure, you may submit the project early. Please ask for confirmation from me that I received it if you are concerned. If you submit it early, you may resubmit if parts are incorrect or missing 75 points: There are 3 tasks to complete involving different questions to be answered and calculations to be made. All information must be arranged on your electronic slideshow according to the instructions or it will not count toward credit! How do I submit my project? It is important that you follow this set of instructions. You will create an electronic slideshow to present your information for your project using Powerpoint (found on your computer). If you need help with creating the slideshow, come to SMART lunch with your gathered information. The slideshow must be sent as an attachment with an to me raven_hayes@iss.k12.nc.us with the subject line saying Trigonometry Project. Any question or information in bold italics has to be included and answered in your Powerpoint At the end, include a references slide for all sources used What will I need? This packet Your computer A graphing calculator For tasks 1 and 2 you will need at least one person helping you A tape measure Chalk A car (with someone to drive it in a parking lot) A jump rope A stopwatch A camera (your phone will do)

2 Task Information Sheet Note: These are used to record an organize your information. Turning these in will not as submitting your project. Keep these to help you make sure everything is answered correctly and to use when making your Powerpoint presentation Task 1: Turning Radius of a Vehicle Because of the difficulty of doing this task, you can do this with 1 or 2 other people from class if you choose, but each one still has to record the information and make their own slideshow You may NOT share data with more than 2 other people or all will be penalized A licensed driver and their car An empty public parking lot (The school after hours would be a safe choice) Chalk A tape measure, a longer one will work better A camera (you can use your phone) Follow these steps, include all answers to questions in your Powerpoint 1.) What is the year, make, and model of the car? 2.) See the diagram below if you are having a hard time understanding what to do Start on a point in the parking lot with plenty of space around the car. While the car is cranked, but in park, steer the steering wheel as far to the left as possible. Using the chalk, mark the starting point of the car right at the side of the front left wheel. Then, draw a long line perpendicular to the direction the front left wheel is facing (see diagram below) (typically needs to be at least 30 feet) After this is done, have the driver slowly drive their car keeping the wheels turned all the way to the left. Be sure that everybody is being safe while doing this. The car shouldn t go farther than half a circle! c.) Mark the ending point of the car right at the side of the front left wheel. Then, draw a long line perpendicular to the direction the front left wheel is facing. This line should eventually intersect with other. If not, extend either/both lines until they do intersect. This point of intersection is the center of Ending Point arc for the car s turn. Both line segments represent the turn radius d.) Draw a straight line connecting the starting point and ending point Distance Traveled (Measure this) e.) Take and add at least two pictures to your presentation showing YOU, the chalk lines, and the car used Starting Point Angle of the Turn Turning Radius (Measure this)

3 3.) Make the following measurements to the nearest inch using the tape measure What is the turning radius to the nearest inch? What is the distance between the starting and ending point of the car? This is all you need to do in the parking lot. The rest can be done using a calculator 4.) On your graphing calculator, hit MODE and hit ENTER while DEGREE is highlighted. Then hit 2nd MODE to quit Use the following formula to calculate the angle of the turn Given r = turning radius, and d = distance between starting and ending points Angle of the turn = cos AB 1 (df ) (2r F ) What was the angle of the turn for the car rounded to the nearest degree? 5.) What was the angle of the turn for car in radians left in terms of π? 6.) Calculate the distance the car traveled along the arc. Using 3.14 for π What was this distance to the nearest inch? 7.) Calculate the area of the sector enclosed by the arc the car drove along and the angle between the starting and ending points. Using 3.14 for π What was this area to the nearest square inch? Task 2: Jumping Rope If you are currently not physically able to jump rope, you may have someone working with you do the jump instead A jump rope A stopwatch (most phones have one on them) A tape measure A person to operate the stopwatch and use the tape measure A camera (you can use your phone) 1.) Stretch appropriately before beginning. Start jumping rope and have another person measure out about how high you are jumping on average. How high were your jumps on average to the nearest inch?

4 2.) Now have the person start timing you jumping rope. Start the watch as soon as you finish making a jump and then have them time you until you have completed 10 jumps continuously in a row. Stop the stopwatch after completing the 10 jumps in a row. Include a picture of you jumping rope (or using the stopwatch if you physically couldn t) in your Powerpoint How long did it take to the nearest 10th of a second to complete 10 jumps? So then how long did it take on average to complete just one jump to the nearest 100th of a second? 3.) Keeping in mind that you started at the low point of the jump on the ground (at 0 inches), write a trigonometric function from the information from 1 and 2 that models your jump height in inches H(t) over time in seconds t My function is H(t) = 4.) Write a short sentence for each explaining how you figured out the amplitude, period, and centerline 5.) Write a new function that represent you jumping rope if you were able to somehow triple your jump height and double how quickly you can make a jump This new function would be H(t) = 6.) Explain why you made the changes you made in complete sentences Your computer Your calculator Task 3: Hours of Daylight in different cities This can be done on your own 1.) On website, find out what city in the world you are assigned My assigned city is 2.) Research the following about your city and include all information in your Powerpoint: c.) What is the current population? What is the latitude for the city? What are two historically or culturally that you found interesting about the city? (Record websites used on your references page) d.) Find and attach at least 2 pictures of the city into your Powerpoint (Record websites used on your references page)

5 3.) Go to the following website: (You need to cite this site) In the search bar type in your city and click search Scroll down until you find a chart that gives the sunset/sunrise and daylength c.) Find June 21st and record the daylength below in hours:minutes:seconds, even if minutes and/or seconds are 0. We are using June 21st because this is the day of the June Solstice. The Daylength on Jun. 21st for my city will be Convert this into all into hours and round to 2 decimal places (It will help to remember that there are 60 minutes in an hour and 3600 seconds in an hour) The Daylength in hours to the nearest hundredth will be d.) Cities above the equator will be experiencing summer and the shortest day of the year while cities below the equator will be experiencing winter and the longest day of the year. Which season will your city begin on Jun. 21st? 4.) The average daylength for any city throughout a year is 12 hours. What part of a trigonometric function would this represent? 5.) How much difference is there between the daylight on Jun. 21st for your city and 12 hours? 6.) What part of a trigonometric function would would the difference represent? 7.) A solar year spans approximately days. What part of a trigonometric function would this represent? 8.) Write a function that represents the daylength D(x) of a particular day after the solstice x, if we started measuring from the day of the solstice. Keep in mind that your city is either starting at the shortest or longest day to decide whether the amplitude should be negative or positive and whether you should be using sine or cosine. My function is D(x) = 9.) After the day of the solstice, what be the date of your next birthday? (Using Jun. 21, 2018 if it happens to fall on Jun. 21) 10.) How many days after this upcoming June Solstice will that day be? 11.) Calculate to the nearest hundredth the daylength in hours for that day. (Be sure the calculator is in radians!) 12.) On your graphing calculator, graph your function and use the value function to show your birthday and the daylength. Use these window settings Xmin=0, Xmax=365, Xscl=1, Ymin=0, Ymax=24, Yscl =1 Take a picture of the screen and post it in your Powerpoint