Xa "Waiting for response fr X + edu.americanhighschool.org/dashboards/ActiveLearning/course-website.asp?action=assignment&Submitid=27110&srloid=27110&rloid=27110&courseid=1486 = 2 American High School Cassidy Williams Dashboard * Management v Reports Опис : Епа спескротс Аррту resources Lessons Assessments Unit 7: Trigonometric Functions End Checkpoint Apply % Unit 7: Mid Checkpoint Apply - Unit 7: End Checkpoint Apply Interactive Tools Unit 7: Trigonometric Functions End Checkpoint Apply Lesson 4 - 7 Algebra 2 Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it. 1. OPEN ENDED Write an equation giving the value of the Cosine function for an angle measure in its domain. Then, write your equation in the form of an inverse function. 2. OPEN ENDED Write the equation of a trigonometric function with a phase shift of -45°. Then graph the function, and its parent graph. 3. Writing in Math If the formula for the temperature Tin degrees Fahrenheit of a city tmonths into the year is given by T = 50 + 25 sin(67), explain how to find the average temperature and the maximum and minimum predicted over the year. 4. Writing in Math Use the information on page 842 to explain how you can predict the behavior of tides. Explain why certain tidal characteristics follow the patterns seen in the graph of the sine function. Your Answer Leave a message Type here to search شا 3:08 PM 8/16/2017 719 x "Waiting for response from CC - Algebra 2 X + o → с = 2 intervisualtechnology.us/uploads/PDFs/ebooks/CC%20-%20Algebra%202/CC%20-%20Algebra%202 Furations 842 - 843 / 1100 that cach of these functions la period of 360 ar 2 radians. That is, the its hx те ans . American High School 500 136,071 145.075 yn 0.5 05 100 O High Tool 0 lo A Paris 90 TOK 2/0" AB Main Ideas Graphigonometric functions. • Find the amplitude and proof wariation of the sine cosine, and tangent functions. New Vocabulary amplitude GET READY for the Lesson The rise and fall of tides can have great impact on the communities and ecosystems that depend upon them. One type of tide is a semidiurnal tide. This means that bodies of water, like the Atlantic Ocean, have two high tides and two low tides a day. Because tides are periodic, they behave the same way each day -10 Tite Ratar 7 SW Lowe 1225-32 15-01 -10 101 270-1) Notice that both the sine and cosine have a mim va value of -1. The amplitude of the graph of a rodicu value of half the difference bxtween its maximim value Har So, for both the sine and cosine functions, the mplitude la ) 2 By examining the values for tan in the table, you function is not defined for 90, 270"............ graph is separated by vertical asymptotes whose intercepts are the values for which ytan is not defined + Graph Trigonometric Functions The diagram below illustrates the water level as a function of time for a body of water with semidiurnal tides. ligh Tide COncepts In Motion Animation algebra.com Viktor LA $ 10 12 14 1. The 2 1 1 Lowice 18. 770" 455 540 * Review Vocabulary Perted the last possible value el o for which f) - R*** In each cycle of high and low tides, the pattern repeats itself. Recall that a function whose graph repeats a basic pattern is said to be periodic To find the period, start from any point on the graph and proceed to the right until the pallern begins to repeat. The simplest approach is to begin at the origin. Notice that after about 12 hours the graph begins to repeat Thus, the period of the function is about 12 hours. To graph the functions y = sin 8y = cos , or y = tan ,use values of expressed either in degrees or radians. Ordered pairs for points on these graphs are of the form (e, sin 8),(C,cost), and (tan), respectively The period of the tangent function is 180° or 1 radians. Since the tangent function has no maximum er minimum value, it has no amplitude Compare the graphs of the secant, cosecant, and cotangent functions to the graphs of the cosine, sine, and tangent functions, shown below. 40 90 109 150 212 225 270 315 y - 5 50 y- 560 D . Vs - 1 . -1 VE } 3 narest tert 05 0.7 09 1 0.2 0 03 09 -1 02 05 y-togel sne va 1 COS 0 0 Vs -1 VE 0 0 3 - 1 180 30 160 ) 330 2 mrest 1 0.7 05 0 -0.5 - 03 -0.5 0 05 05 1 VS 1 1 V's -V's . 3 1 Vs -Vs -1 M D 1 1 11 -12 - 1 0 1 1 -11 -1 Ipre Notice that the period of the servant and consecant functions is 367 or 2t radians The period of the cotangent is 180° or s radians. Since none of these functions T III A g Type here to search O e E w O x TE 3:09 PM 8/16/2017 719
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