Assignment 1 1.1: Sinusoidal Graphs Score: ("HE 0:3 answered Progress save I Question I v B A population of rabbits oscillates 21 above and below average during the year, hitting the lowest value in January.r [t - D]. The average population starts at 950 rabbits and increases by 200 each year. Find an equation for the population. P. in terms of the months since January, t. Pm = . Question 2 v E 0.11 pt '0 3 Z 99 You are strongly encouraged to do all three parts. However, only part (b) is entered here to be graded. (a) Make a scatter plot of the data. (b) Use a graphing calculator to find the sine function that best fits the data. yit) = |_ i (c) Graph the function you found in part [b] together with the scatter plot. [How well does the curve fit the data?) i D L E E iiil Comments: Enter your answer as an expression, and be sure your variables match those in the question. To err on the side of caution, enter at least 4 decimaL places for each value from the calculator {and remember to round appropriately]. 0 Question 5 v B Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 85 degrees and the low temperature 0165 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. 13(5) =| . Question 6 v B The temperature in Latlaville varies between 12 and 59 degrees Fahrenheit during a typical year. Assume that the temperature on July 1 is 59. Find an equation for the temperature [denoted T] in Lallaville in terms of months since Dec 1 [denoted Jr]. Tm = ' . Question 7 v ( > The temperature on a certain planet oscillates according to the function T(z] = 4.1coa(3.27r:r) where T is meaSured in dugreez and a: in sekunds. Find the temperature at the times indicated in the table. Report answers accurate to at least 4 decimal places. Assignment 11.2: Law of Sines Progress m Score: DH? U-' I? answered '. Question 1 1' E Acommunicatien tower [the side CE) is located at the top {the point C] of a steep hill. The angle of inclination of the hill is 58 degrees. Aguy wire is to be attached to the top {the point B] of the tower and to the ground [the point A], 9? n1 downhill from the base of the tower {the side AC}. The angle ZBAC' is 12 degrees. Find the length of cable (the side AB] required for the guy wire. Your answer isI m; . Question 2 1' Using the Lawr of Sines to find a triangle with one obtuse angle if .111 45",:1 24, b 2'5. If no answer exists. enter DHE for all answers. [B is I I degrees; .40 is I I degrees; c = I I : Assume /A is opposite side a, ('3 is opposite side b, and /C is opposite side 6. . Question 4 v 30 x Given the triangle , find the length of side I using the Law of Sines. Round your final answer to 4 decimal places. I . Question 5 1' To find the distance across a river. a surveyor choose points A and B. which are 243 yd apart on one side of the river. She then chooses a reference point If on the opposite side of the river and finds that ZBAC E 84' and [ABC 2 49'. A 2433i 3 I. '7 NOTE: The picture is NOT drawn to scale. Approximate the distance from point A to point C. distance = yd Find the distance across the river. height = yd Enter your answer as a number; your answer should be accurate to 2 decimal places. 0 Question 7 v c > Acommunications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 141A guy wire is to be attached to the top of the tower and to the ground, 133 m downhill from the base of the tower. The angle formed by the guy wire is 10'. Find the length of the cable required for the guy wire. NOTE: The picture is NOT drawn to scale. length of guywire = m Enter your answer as a number; your answer should be accurate to 2 decimal places. . Question 3 v Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such than ZC'AB 51.3". Find the distance across the lake from A to B. B C 393 m A NOTE: The triangle is NOT drawn to scale. distance - n1 Enter your answer as a number; your answer should be accurate to 2 decimal places. I. Question 9 v Given a triangle with angle A - 101 degrees and sides a - 39 and b - 12. Find side c. . Question 10 V ( > Given the triangle below, find the angle A and length of side it Note: picture is NOT drawn to scale, but you can assume an angle that appears acute is acute and angie that appears obtuse is obtuse. 22 39 x A = ' ' degrees x - l l . Question 11 ' Using the Law of Sines to solve the all possible triangles if /A = 100,a = 31,-!) = 16. If no answer exists. enter DNE for all answers. {13 is l ' degrees 0 is l I degrees c = i l Assume /A is opposite side a. /Bis opposite side :5, and /C is opposite side a. Question Help: E] Video 0 Question 12 v 8 0H pt E To estimate the height of a mountain. two students find the angle of elevation from a point at ground level] i) 720 meters from the base of the mountain to the top of the mountain is ,5 59'. The students then walk a 1350 meters straight back and measure the angle of elevation to now be Ct 300, If we assume that the ground is level, use this information to estimate the height of the mountain. The height of the mountain is meters. . Question 14 ' 3 OH I In the triangle shown, I /A 70 degrees - /B = 59 degrees a length AB 8 Find the measures of the other sides and angles ZC - I degrees l | length AC = ' {Round your answer to three decimal places] length BC =' ' (Round your answer to three decimal places] I. Question 15 v Use the Law of Sines to solve for the remaining sideis] and angleisi of the triangle if a 100",a 45,5 50. Round to two decimal places. As in the text. (ma), (,3, b) and (ne) are angle-side opposite pairs. If no Such triangle exists, enter DNE in each answer box. 15 I I degrees 7=I I degrees 4:; 10.5 . Question 1 0/1 pt 9 3 99 0 Details 104 Based on the graph above, determine the amplitude, midline, and period of the function Amplitude: Period: Midline: y = Question 4 0/1 pt 9 3 99 0 Details Find a function of the form y = Asin(kx) + Cory = Acos(kx) + C whose graph matches the function shown below: Leave your answer in exact form; if necessary, type pi for 7.. Question 5 0/1 pt 9 3 99 0 Details Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 68 and 32 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t) = . Question 6 Go/1 pt 9 3 99 0 Details A ferris wheel is 10 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y = meters What is the Period? minutes How High are you off of the ground after 1 minutes? meters .Question 14 Go/1 pt 9 3 99 0 Details 8- -6 -5 -4 3 -2 -1 1 12 3 4 6 Write an equation for the function graphed above. y =. Question 15 0/1 pt 9 3 99 0 Details -6 -5 -4 -3 -2 -1 2 3 4 5 6 -3 The graph above is a graph of what function?0 Question 1? v E10" pt 0 3 1393 G) Details Match each graph with its equation. Not all equations will be used. Assignment 10.7: Solving Trigonometric Equations Score: 6.?53'16 1516 answered . Question 8 v ( 3 Solve 5111(3) [1.17 on U 1: I s': 211. There are two solutions, hand B, with A Solve 251n2{:o) Sink} l = U for all solutions. :I: = I I +2k1r : Select an answer V Give your answers as exact values in a list separated by commas. . Question 15