Trigonometry Questions and Answers

3 22 0 5 4 3 2 1 1 2 3 4 5 6 2 H 3 Identify the function whose graph appears above f x

Find all solutions to each of the following triangles 7 A 38 a 41 feet b 54 feet 8 A 43 a 31 feet b 37 feet 9 A 112 2 a 43 centimeters b 22 centimeters 10 B 30 b 42 centimeters a 84 centimeters 11 B 118 b 68 centimeters a 92 centimeters 12 A 124 3 a 27 centimeters b 50 centimeters 13 A 142 b 2 9 yards a 1 4 yards 14 A 65 b 7 6 yards a 7 1 yards 15 C 26 8 c 36 8 kilometers b 36 8 kilometers

6 Trigonometry Homework Lesson 2 MULTIPLE RIGHT TRIANGLE PROBLEMS 1 Calculate the length of BC 30 10 cm 50 8 cm C 2 Calculate the measure of LABC a 44 C

4 To determine the distance across a marsh AB on diagram a surveyor measures LACB to be 65 Determine the length of the marsh 47m

tan 0 cot 0

1 sin 0 3 cot 1 2 tan 0 sec csc e 2

sin a sin sin a sin cos a cos C B

Multiple Choice Circle the most appropriate answer 1K mark each 1 The tangent ratio is between which two sides Opposite Adjacent Opposite b Hypotenuse Adjacent c Hypotenuse Adjacent d Opposite 2 Given the triangle below what would be the most appropriate solving technique to find x a Sine Law b Cosine Law c SOHCAHTOA d Pythagorean Theorem 6 3

10 Find the height h of the mountain to the nearest kilometer Note AABD is not a right triangle B 38 53 D 33 42 6 km A

5 4 3 1 4 The curve above is the graph of a sinusoidal function It goes through the points 5 0 and 1 0 Find a sinusoidal function that matches the given graph If needed you can enter 3 1416 as pi in your answer otherwise use at least 3 decimal digits f x

Determine whether the sequence an arctan 9n2 converges or diverges If it converges find the limit Converges y n Limit if it exists blank otherwise

8 of 19 Given the trigonometric ratios in the following table determine the corresponding angle 8 rounded to the nearest degree and the other two trigonometric ratios rounded to four decimal places wherever applicable a e sin e cos e tan 0 5299

Find the exact values of the six trigonometric functions of the angle e shown in the figure y sin e cos e tan e CSC 0 sec 0 3 9 X

5x List all points on the graph of y tan x on the interval 2 that have a y coordinate of 3 2

wo sides of a triangle have lengths 11 m and 18 m The angle between them is increasing at a rate of 2 min How fast is the length of the third side increasing when the angle between the sides of fixed length is 60 Round your answer to three decimal places m min

EXAMPLE 5 A man walks along a straight path at a speed of 5 ft s A searchlight is located on the ground 12 ft from the path and is kept focused on the man At what rate is the searchlight rotating when the man is 5 ft from the point on the path closest to the searchlight SOLUTION We draw the figure to the left and let x be the distance from the man to the point on the path closest to the searchlight We let be the angle between the beam of the searchlight and the perpendicular to the path We are given that dx dt 5 ft s and are asked to find de dt when x 5 The equation that relates x and 0 can be written from the figure X tan 0 x tan 0 Differentiating each side with respect to t we get SO dx dt de dt de dt dx dt 5 When x 5 the length of the beam is 13 so cos 0 12 and 13 de dt The searchlight is rotating at a rate of rad s

A baseball diamond is a square with side 90 ft A batter hits the ball and runs toward first base with a speed of 28 ft s 90 ft a At what rate is his distance from second base decreasing when he is halfway to first base Round your answer to one decimal place ft s b At what rate is his distance from third base increasing at the same moment Round your answer to one decimal place ft s

Verify the identity cot csct csct sint To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step cot 2 csct csct Do not simplify csct sint

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval and approximate the solutions to four decimal places Enter your answers as a comma separated list 3 sin 9 sint 5 0 2 2

5 Show how you could set up and find the exact value of cos COS 57 COS 4 2 2 cos x cos COS 4 COS X TU 2 2 in two different ways

Given a capacitor of C 3 F calculate the current going through the capacitor during the interval t1 st st2 when the capacitor voltage is as described in Fig 6 12 Assume V1 10V V2 5V and t1 8 S and t2 13 S Note values might be different than the above problem v t V A V1 V2 O Figure P6 12 t2 t3 t1 1 ps

1 The angle of elevation of the sun is decreasing at rad h How fast is the shadow cast by a building of 4 height 54 m lengthening when the angle of elevation of the sun is 4

Problem 1 1 cos 2x sin 2x ta

Verify the following identity sin t 1 cos t cost cot t Cost cot t

Congress is now thinking about banning TikTok or forcing its sale to a US based company likely one of the tech giants If this happens what market failure will be worse Adverse selection O Market power O Externalities O Moral hazard

csc e cot e sec e

List all points on the graph of y tanx 5 on the interval 37 that have a 2 y coordinate of 3

In a proposed business venture a businesswoman estimates there is a 65 chance she will make 59 000 and a 35 chance she will lose 53 000 Determine her expected value Her expected value is

sin x c COS I sec a csc z tan r cot a

the different strategies verify the following identity 1 sin x CSC X 1 CSC X

function The population sizes of many animal species rise and fall over time Suppose that the population size of a certain species can be modeled by the following p t 3390 1190 cos 1 41 In this equation p t represents the total population size and t is the time in years Find the following If necessary round to the nearest hundredth Amplitude of p Period of p years Frequency of pcycles per year X 5

Write the equation of a sine or cosine function to describe the graph KIM 16 2 3 16

Find Vec in the circuit in Fig P2 20 Given the voltage reading on the resistors of V1 4 V V2 9 V and V3 7 V a b ww V2 V1 12 V 3 V V3 ww g 2V f V4 e Figure P2 20 Notes on entering solution Enter your solution in Volts V Enter your solution to 2 decimal places Do not include units in your answer ex 5 V is entered as 5 00 Reminder Vec means that e is the high side and c is the low side

A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 12 in and period 0 1 seconds Its displacement d from sea level at time 0 seconds is 12 in and initially it moves upward Note that upward is the positive direction Give the equation modeling the displacement d as a function of time d 0

1 solve for x tan 2 Frank tan cos esc x 1 COS 2X csc x

sin 2 cos 2 theta 1 sin theta

In the right triangle below p 30 and b 5 3 Find a a b P 10 10 3 10 2 15

A rain gutter is to be installed around a house whose foundation is shown to the right Find the perimeter of the house then find the total cost of the gutter The gutter costs 4 69 per ft 21 ft The perimeter is 19 ft 29 ft 20 20

Verify the following identity 1 sec a tan 2 tan Which of the following statements establishes the identit O A O B OC 1 cos a 1 sec tan 2 2 tan tan 2 1 cos 1 sec a 2 tan tan 2 cos 1 sin 1 sec a tan

X 4 10 pt Find the solution using the substitution y ux or u x 0 dx

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 List the sample space Choose the correct answer below w Appetizer Cheese plate C Vegetable tray V Guacamole G O A CFB CFK CFP CWB CWK CWP VFB VFK VFP VWB VWK VWP OB OC D Beverage Fruit punch F Water W Dessert Brownies B Cake K Pie P CFB CFK CWB CWK VFB VFK VWB VWK GFB GFK GWB GWK CFB CFK CWB CWK CB CK VFB VFK VWB VWK VB VK GFB GFK GWB GWK GB GK 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 The probability is Simplify your answer

4 The bearing of Chris from Al is N70 E and the bearing of Ben from Al is S50 E If the bearing of Chris from Ben is N20 W and Chris is 20m from Al how far is Ben from AI 5 points Total 55 50

Find the exact value of the composition if possible Enter the answer in terms of pi as needed Do not enter a decimal 4 approximation cos cos 3 1

If f x 4x 3 compute the first second and third derivative of f x f x f x f x Submit Answer

Determine the exact values of the six trigonometric functions for 0 if 7 5 is a point on the terminal side of 0 Reduce fractions and simplify radicals Do not use decimals Q1 1 50 Points sin 9 points cos 9 points

Determine the relative phase relationship of the two waves u1 t 10 cos 377t 43 V u2 t 10 cos 377t 117 V Notes on entering solution Enter your solution with respect to u2 t leads u1 t by Enter your solution in degree Do not include units in your answer ex 5 is entered as 5

Calculate current across the capacitor shown in Fig P8 6 if the voltage input is v1 t 30 cos 262t 25 V v t Figure P8 6 i t ex 5 is entered as 5 C 1 F For a current i t C cos wt P enter the value of the phase angle P be sure that your answer is between 180deg to 180deg Notes on entering solution Enter your solution in degrees Have your current in cosine format Do not include units in your answer

The previous experiment is not bound to involve only two forces Suppose you were to add two force vectors F 0 98 N 20 and F 1 96 N 120 We want to know what a third force F3 would be to obtain a zero net force 98 1 96 x C

Show all calculations tes of point P in the figure below are as shown What is the moment of force F about point P 25 Points P 90 0 F 1 200 lbs 30 X J s in go 905in 30 45 1200 in30 Efy 20ocos 30 1200 45 5

Y P 45 45 F3 10 000 lbs F2 F1 23 000 lbs 1