Assignment 1 1.1: Sinusoidal Graphs Score: (N8 {ll-'8 answered Progress save 0 Question 1 v B A population of rabbits oscillates 21 above and below average during the year, hitting the lowest value in January.r [t - U}. 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 The displacement of a mass suspended by a spring is modeled by the function Mt) : Tsin(11mt) Where h(t] is measured in centimeters, and t is measured in seconds Find the: . . Amplitude: ' cm Period: [ ' seconds Frequency: ' Hz {a} Make a scatter plot or the data. [b] Use a graphing calculator to find the sine function that best fits the data. W) l {cl Graph the function you found in part (in) together with the scatter plot. {How well does the curve fit the data?) D a m w H' H: t: \D L as M I L Comments: Enter your answer as an expression, and be sure yo-Jr 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 4 ' B 0J1 pt '5'.) 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. ya) = i i (c) Graph the function you found in part (b) together with the scatter plot. [How well does the curve fit the data?) .L i D 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]. I Question 5 v E Outside temperature over a day can be modelled as a sinusoidal function. Suppose you knowr the high temperature for the day is 35 degrees and the low temperature of 65 degrees occurs at 5AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D3) = . Question 6 The temperature in Lallaville 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 7) in Lallaville in terms of months since Dec 1 (denoted x). T (x) = . Question 7 The temperature on a certain planet oscillates according to the function T(x) = 4.1 cos(3.2TI) where T is measured in dugreez and IT in sekunds. Find the temperature at the times indicated in the table. T(x) 0 0.25 0.5 0.75 1.25 Report answers accurate to at least 4 decimal places.Assignment 11.2: Law of Sines progress m Score: DH? U-'l? answered . Question 1 ' E Acommunication 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 13110 is 12 degrees. Find the length of cable (the side AB] required for the guy wire. Your answer isI rn; 0 Question 2 9 ( ) Solve the triangle ABC if b : 125,c : 163, LB : 40". a = I I {IA I I degrees; {LC _ I I degrees; Assume Ad is opposite side a. .ZBis opposite side b, and [C is opposite side 6, and that the triangle is acute. . Question 3 v Using the Lawr of Sines to find a triangle with one obtuse angle if .{A 45",:1 24, b 26. If no answer exists. enter DNE for all answers. L'B is I I degrees; .50 is I I degrees; C = I | ; Assume {/44 is opposite side a, /.B is opposite side 5', and /C is opposite side (2. . Question 4 v 30 x Given the triangle , find the length of side 1: using the Law of Sines. Round your final answer to 4 decimal places. 2! . Question 5 v A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5.3 mi apart, to be 28' and 49", as shown in the figure. = I K .. '3 x ~ 49- 2, \\ I, \ r x f I} X (I - \s X 3.3 rm' '\ A 3 NOTE: The picture is NOT drmvn to scaie. Find the distance of the plane from point A. distance from A =| ' mi Find the elevation of the plane. height =| \ mi . Question 6 ' 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 C on the opposite side of the river and finds that [BAG 3: 84 and [ABC 2 49'. A. 243J'a' B l' " 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. '. Question 7 v Acommunications tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is 74'. A guy wire is to be attached to the top of the tower and to the ground, 138 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 guy-wire = m Enter your answer as a number; your answer should be accurate to 2 decimal places. . Question 8 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 ZCAB 513. Find the distance across the lake from A to B. B C 393 m 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. . Question 9 v Given a triangle with angle A - 101 degrees and sides a - 39 and b - 12. Find side c. . Question 10 V ( > Iiiiiien the triangle below, find the angle A and length of side in: Note: picture is NOT drawn to scaie, but you can assume an angle that appears acute is acute and angte that appears obtuse is obtuse. 22 I9 I A = l ' degrees I 'l i 0 Question 11 v Using the Law of Sines to solve the all possible triangles if /A = 1000,0l = 31,:l? = 16. If no answer exists, enter DHE for all answers. 113 isl ' degrees /_'C is l ' degrees c = l | Assume /A is opposite side a. ('3 is opposite side b, and /C is opposite side c. Question Help: E] Video . Question 12 v 8 0H pt '5: To estimate the height of a mountain. two students find the angle of elevation from a point at ground level} 5 720 meters from the base of the mountain to the top of the mountain is ,3 59!. The students then walk a 1350 meters straight back and measure the angle of elevation to now be a 30". 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. I Question 14 v B on I In the triangle shown, I /A TU degrees - /B = 59 degrees a length AB _ 8 Find the measures of the other sides and angles EC I I degrees length AC = I (Round your answer to three decimal places] length BC =I I (Round your answer to three decimal places} I. Question 15 1'