Trigonometric equations Questions and Answers

Given the following voltage and current i t 5 sin 377t 57 A u t 10 cos 377t 41 V Determine the phase relationship between i t and u t Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degree Do not include units in your answer ex 5 is entered as 5

Given the following voltage and current i t 5 sin 377t 48 A u t 10 cos 377t 52 V Determine the phase relationship between i t and u t Notes on entering solution Enter your solution with respect to V leads i by Enter your solution in degree Do not include units in your answer ex 5 is entered as 5

8 Nancy is in her apartment on the sixth floor of a building She spots two cars that are parked 10 ft apart If she measures the angle of depression to the closest car to be 50 and then the further car to be is 38 How far is the first car parked from the base of her apartment building to the nearest foot

1 Find cos 105

9 A 10m ladder leans against a vertical wall at an angle of 63 Find the height the ladder reaches up the wall Draw and label a sketch to represent this situation

2 Find sin 75

13 A A radio tower is located 400 feet from a building From a window in the building a person determines that the angle of elevation to the top of the tower is 36 and that the angle of depression to the bottom of the tower is 23 How tall is the tower B There is lightning rod on the top of a building From a location 500 feet from the base of the building the angle of elevation to the top of the building is measured to be 36 From the same location the angle of elevation to the top of the lightning rod is measured to be 38 Find the height of the lightning rod C A 400 foot tall monument is located in the distance From a window in a building a person determines that the angle of elevation to the top of the monument is 18 and that the angle of depression to the bottom of the monument is 3 How far is the person from the monument

x fly ngly Consider the blue horizontal line shown above click on graph for better view connecting the graphs f y sin 2y and x g y cos ly Referring to this blue line match the statements below about rotating this line with the corresponding statements about the result obtained 1 The result of rotating the line about the x axis is 2 The result of rotating the line about the y axis is 3 The result of rotating the line about the line y 1 is 4 The result of rotating the line about the line x 2 is 5 The result of rotating the line about the line x is 6 The result of rotating the line about the line y 2 is 7 The result of rotating the line about the line y 8 The result of rotating the line about the line y A a cylinder of radius y and height cos 1y sin 2y B an annulus with inner radius 2 sin 2y and outer radius 2 cos 1y C a cylinder of radius y and height cos 1y sin 2y D a cylinder of radius 1 y and height cos ly sin 2y E a cylinder of radius 2 y and height cos 1y sin 2y F a cylinder of radius y and height cos 1y sin 2y G an annulus with inner radius cos 1y and outer radius sin 2y is H an annulus with inner radius sin 220 and outer radius co

Assume a is opposite side a is opposite side b and y is opposite 32c56 5xx s 66 a 42 b 32 c 56 5xx

2 2 2 t ny t ty y dt 11 x 1 x 1

Simplify 3 52 19 17 12 9 11 8

20 24 If tan and cot for 21 7 a second quadrant angle x and a third quadrant angle find the following a sin a B b cos x B c tan B d sin B e cos f tan B

Use substitution to determine whether the given x value is a solution of the equation cos x sin 4x x 3 O X T 13 3 is not a solution of the equation x is a solution of the equation

Evaluate Feedback Print Consider the f x cos Bx function shown in the figure in blue color What is the value of parameter B for this function This parameter is called angular requency in physics and it is denoted by w 335 0 5 As a reference the g x cos x function is shown in red color and green tick marks are drawn at integer multiples of n Submit Answer Tries 0 99

To protect an elm tree in your backyard you need gypsy moth caterpillar tape around the trunk The tree has a 2 3 ft diameter What length of tape is needed Use 3 14 for The length of the tape is approximately Simplify your answer Type a whole number or a decimal Round to

Consider the wheel to the right If the wheel is spun and each section is equally likely to stop under the pointer determine the probability that the pointer lands on an even number given that the color is purple Note that the purple sectors are the sectors numbered 10 12 5 7 and 8 9 10 11 12 8 7 2 6 5 3 4 The probability that the pointer lands on an even number given that the color is purple is Type an integer or a simplified fraction

From the list shown Steve will purchase one appetizer one beverage and one dessert at random to bring to a party Complete parts a through e www Appetizer Cheese plate C Vegetable tray V Guacamole G The probability is VRTTU OTT U UN U V V V V V V V V VIT U ON D CFB CFK CFP CWB CWK CWP VFB VFK VFP VWB VWK VWP GFB GFK GFP GWB GWK GWP c Determine the probability that Steve selects the cheese plate for the appetizer 1 3 Simplify your answer d Determine the probability that Steve selects the water and the brownies The probability is Simplify your answer Beverage Dessert Fruit punch F Brownies B Water W Cake K Pie P

Find the Wronskian for the set of functions e x e 2x

An equal tangent sag equal tangent vertical curve with a negative initial and a positive final grade is designed for 55 mi h The PVI is at station 240 00 and elevation 122 ft The PVT is a station 242 30 and elevation 127 75 ft What is the station and elevation of the lowest point on the curve

Write the equation of a sine or cosine function to describe the graph Ik 5 y FR 45 27 3 47 5 0 B 0 0 X

In the following diagram suppose side e 9 02 m and side f 1 74 m side j 2 12 m Find the Length of side i e g f ct hundredth if needed Be sure to include proper

Given i t 5 cos 430t 120 A determine the period of the current Notes on entering solution Enter your solution in seconds s Enter your solution to the nearest ten thousandth of a second Do not include units in your answer ex 5s is entered as 5 0000

Lorrie places a 29 foot ladder against the side of a building with the bottom of the ladder 20 feet from the base of the building How high up the wall does the ladder reach The ladder reaches feet up the wall Round to the nearest whole number as needed 20 ft 29 ft ladder

1 5 N 2 0 5 1 of 17 1 5 2 25 3 3 5 The two lines intersect where x br 4 5 5 5 5 6 Given the graph of the lines y 4x and y 1 5x 12 5 where do the two lines intersect 6 5 and y 7 5