Trigonometry Questions and Answers

The triangle in the figure may require the law of sines or the law of cosines Choose the appropriate method and solve the triangle A 11 Use decimal notation Give your answers to two decimal places Include the degree symbol in your answers where needed If two solutions exist just pick one and either will be counted as a correct one Enter DNE if the triangle has no solution B 15

Assignment 9 Problem 6 1 point Find the measures of the three angles in radians of the triangle with the given vertices D 1 1 1 E 1 4 2 and F 4 2 8 1 ZD 2 ZE 3 LF

Assignment 9 Problem 13 1 point The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB as indicated in the diagram So the distance from P 2 5 1 to the line through the points A 0 3 5 and B 5 5 2 is

A freshwater pipeline is to be run from a source on the edge of a lake to a community on an island 3 miles offshore as shown in the figure Answer the questions that follow 3 miles X x 20 x 20 miles Som A If it costs 1 4 times as much to lay pipe in the lake as it does on land what should x be in miles to minimize th total cost of this project miles Round to the nearest tenth as needed

Two planes leave an airport at the same time Their speeds are 130 miles per hour and 110 miles per hour and the angle between their courses is 48 How far apart are they after 1 5 hours Round your answer to the nearest whole number mi

verity the following identity 2 tan 0 1 1 tan 0 2 Which of the following four statements establishes the identity tan 0 1 tan 0 1 sec 0 1 tan 0 O A B cos 20 O C cos 20 sin 0 cos 0 cos 20 2 sin 0 cos 0 tan 2 D cos 20 2 sin 0 cos 0 cos 20 sin 20 cos 0 sec 0 tan 0 1 2 0 1 2 CSC 0 tan 2 0 1 csc 0 tan 0 1 1 tan 0 tan 0 1 2 2 1 tan 0 tan 0 1 1 tan 0

csc 0 1 csc Choose the correct proof below OA csc 0 OB csc 0 cos 0 cot 0 OC csc 0 1 csc 0 1 csc 0 1 csc 0 1 sin 0 sin 9 sec 0 1 sin 0 ein 0 1 sin 0 2 sin 0 sin 0 sin 0 1 sin 0 sin 0 1 sin 9 in 201 sin e 2 cos e cos sin 0 cos 0 cos 0 cot 0 cos 0 cot cos 0 cot

sec x csc x tan x cot x hoose the correct proof below A sec xcsc x tan x 1 1 cOS X sin x cos x cot x 2 1 sin x sin x cos x cos 2 sin x OC sec x csc x tan x 1 1 X cot x COS X 1 sin sin x X sin x cos x cos x 2 sin x cos x sin x COS X OB sec x csc x tan 1 1 cOS X sin x 1 sin x sin x cos x 2 COS X cot x sin x cos x D sec xcsc x tan 1 1 COS X sin x sin x cos x 2 1 s sin x sin x cos x 2 cos X cot x

1 cot 0 sin 0 1 Which of the following shows the key steps in proving the identity OA 1 cot20 sin 2 0 csc 0 sin 0 1 sec 0 sin 0 sin 0 OB 1 cot 0 sin 0 sin 0 cot 0 sin 0 sin 0 cos 0 1 OC 1 cot 0 sin 0 tan 0sin 0 2 sin 20 1 cot 20 OD 1 cot 0 sin 0 cos 0 sin 20 sin 0 cos 0 sin 0 sin 2 1 1 cos 20 sin2 0 cos 0 1

Use a double angle formula to find the exact value of the given expression 2 cos 2 3r 8 3r 2 cos 2 1 1 8 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Prove the given identity cot x secx csc x tan x Choose the correct proof below O A cot x sec X CSC X 1 COS X 1 cos x sin x O C sin x 2 1 cos x sin x cos X 2 sin X sin x cos x tan x cot x sec x csc x COS X sin X sin x cos x 2 1 cos X sin x cos X 2 sin x tan x OB O D cot x sec XCSC X COS X 1 1 sin x COS X sin x cos X sin x 2 1 Cos X sin x cos X 2 sin x tan x cot x sec Xcsc X COS X sin x 2 1 cos x sin x cos x 2 sin X sin x cos x tan x

You may need to use the appropriate appendix table or technology to answer this question The Economic Policy Institute periodically issues reports on workers wages Suppose the institute reported that mean wages for male college graduates were 37 39 per hour and for female college graduates were 27 83 per hour in 2017 Assume the standard deviation for male graduates is 4 60 and for female graduates it is 4 10 Round your answers to four decimal places a What is the probability that a sample of 40 male graduates will provide a sample mean within 1 00 of the population mean 37 39 b What is the probability that a sample of 40 female graduates will provide a sample mean within 1 00 of the population mean 27 83 c In which of the preceding two cases part a or part b do we have a higher probability of obtaining a sample estimate within 1 00 of the population mean why O part b because the standard error is lower O part a because the standard error is lower O part b because the standard error is higher O part a because the standard error is higher d Calculate the amount that is 0 60 less than the population mean of 27 83 What is the probability that a sample of 130 female graduates will provide a sample mean less than this amount

In If it is known that sin a alue of sin a B 12 13 0 a 0 a that cos B 2 5 37 2 find the exact and that cos it rose to oulisy 5 2 202 nie 205 m 20 10

Verify the identity 2 CSC x cot x 1 2 cot x Which of the following four statements establishes the identity O A csc 2 x cot x 1 cot2x cot x 1 2 cot x OB csc x cot x cot2x 1 cot x 1 2 cot x OC csc X cot x 1 cot x cot x 1 2 cot x OD csc x cot x 1 1 2 cot x

Prove the given identity sec 0 OA sec 0 1 sec 0 Choose the correct proof below B sec 0 OC sec 0 OD sec 0 tan 0 sin 0 1 sec 0 1 sec 0 1 sec 0 1 sec 0 1 cos 8 1 cos 0 1 cos cos cos cos 1 cos 0 cos 8 sec 0 cos 1 cos 0 2 2 1 cos 0 cos 0 2 COS 0 cos 0 1 1 cos 2 0 cos 2 sin 0 cos cos 0 2 sin 0 sin 0 cos 0 cos 2 sin 0 tan sin 0 tan 0 sin 0 tan 0 sin 0 tan sin 0

Prove the given identity CSC 0 1 cos 0 1 Which of the following shows the key steps in proving the identity OA csc 2 0 1 cos 0 csc 0 csc 0 cos 0 csc 0 cot 0 1 OB csc 20 1 cos 0 csc 0 sin 0 csc 0 Oc csc 2 0 1 0 1 cos 0 cos 0 csc 0 cot 0 csc 0 OD csc 2 0 1 cos 0 sec 0 1 cos 20 1 tan 0 sin 0 sin 0 2 sin 0 2 sin 0 1 1 sin 20 csc 0 cot 0 1 2

3 Use Green s Theorem to evaluate the line integral of F x y 4x y on C the boundary of x y 0 y sinx 0 x oriented counterclockwise 8 points

20 Identify the graph below that corresponds to each given slope and y intercept a slope 3 y intercept 2 1 b slope y intercept 2 c slope 3 y intercept 2 1 d slope y intercept 2 Graph A 2 20 3 Graph C y 0 3 X Graph B 4 2 Graph D y

4 A paper cup is in the shape of a cone as shown in Figure What is the surface area of the cup 3 60 in 3 50 in Ans S 22 3 in 5 A glass prism used in the study of optics has a right triangular base The legs of the triangle are 3 00 cm and 4 00 cm The prism is 8 50 cm high What is the total surface area of the prism See Figure

1 point Suppose a line is given parametrically by the equation Then the vector and point that were used to define this line were V p L t 0 2t 3 3t and

Z 1 2dz C z sec 4 Question 11 Find 1 C z 1 sec 4 4 7 CCW

ment Score 13 of 13 Macmillan Learning 0 While diving off the coast of California a diver spots a large shark Using a laser device she finds that the distance to the tail of the shark is 30 feet and the distance to the head is 35 feet The angle between the two measurements is 20 The figure is shown How long is the shark Diver 20 Shark s length 35 30 Shark Use decimal notation Give your answer to at least one decimal place Resources Ly Give Up7 feet

Solve the given triangle Use degree measure A 25 B 19 B Use decimal notation Give your answer to three decimal places Include the degree symbol in your answers 16

Write the equation of a sine or cosine function to describe the graph FIN 70 2 RIN 2 3 2 2 fela 5 T 0

The Mach number M of an airplane is the ratio of its speed to the speed of sound When an airplane travels faster than the speed of sound the sound waves form a cone behind the airplane see figure The Mach number is related to the apex angle 8 of the cone by sir a Find the angle that corresponds to a Mach number of 1 0 X b Find the angle that corresponds to a Mach number of 2 5 Round your answer to four decimal places 8 radians c The speed of sound is about 760 miles per hour Determine the speed of an object having the Mach numbers in parts a and b Mach number of 1 760 mph 1900 Mach number of 2 5 mph d Rewrite the equation as a trigonometric function of 0

ANSWER c 6 cos 5x 1 4 7

Problem 4 Find the exact value of the expression or write an algebraic expression that is equivalent to the expression Show all your steps a arccos COS b sin arctan c sec arcsin 2 2 ese arctan 2 d csc e sec arcsin x 1 f cos arctan 2x

lem 1 Suppose that cos lem 2 Suppose that sin 0 25 12 13 and 0 T Determine the values of sin COS and tan

Problem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20 25

Problem 1 Suppose that cos 0 7 and tan 0 0 Determine the values of sin 20 cos 20 and tan 20 25

The three right triangles below are similar The acute angles LL LR and LZ are all approximately measured to be 62 4 The side lengths for each triangle are as follows Note that the triangles are not drawn to scale 19 73 cm L 62 4 9 15 cm J 17 48 cm K KL JL 118 38 cm P Osine O cosine Otangent R 62 4 177 57 cm che venn 62 4 54 9 cm 157 32 cm 104 88 cm Q a For each triangle find the ratio of the length of the side adjacent to 62 4 to the length c the hypotenuse Note that side adjacent cannot also refer to the hypotenuse Round your answers to the nearest hundredth QR PR X YZ XZ b Use the ALEKS Calculator to find sin 62 4 cos 62 4 and tan 62 4 Round your answers to the nearest hundredth sin 62 4 cos 62 4 tan 62 4 c Which trigonometric function gives each ratio of sides in part a 82 35 cm Y

An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up The ladder makes an angle of 66 with the ground Find the length of the ladder Round your answer to the nearest tenth of a foot if necessary

1 The ship in the figure is at sea 12 miles from the lighthouse The light beam from the lighthouse must rotate through 70 to be seen by the people on the ship Lighthouse How close is the ship to the shore i e what is the distance to point P on the shore ANSWER b 70 70 12 miles 12 miles P There is a second lighthouse on the shore as shown in the figure The light beam from the second lighthouse must rotate through 65 to be seen from the ship What is the distance between the two lighthouses bits Lighthouse 1 Lighthouse 2 Shoreline Ship Shoreline 65

7 Consider the following diagram constructed in Quadrant I of the Unit Circle a 0 1 C b Find a b c and d in terms of 8 Show all work d

TASK 1 FENCING PART A Here is a sketch of your backyard 24 65 ft Work Space 14 8 ft How much fencing will you need Backyard 24 65 ft 14 8 ft buy Find the perimeter using ADDITION Show your work Circle and Label your answer

O Macmillan Lea 75 0 5 x sin 4x COS 0 25 0 0 25 T 0 25 8 0 5 Use the graph to find the solution of the equation on the specified interval 7 if 0 x Use decimal notation Give your answer to two decimal places 0 75 X powered W desmas

Entered AC BD h 9 Answer Preview Consider the graph G shown below a AC f BD At least one of the answers above is NOT correct b e Result d incorrect incorrect Determine whether each of the following is a perfect matching and whether it is a partial matching a h b g e f A Is a perfect matching A Is a partial matching a b b c c d d e e f f g g h h a a b c d e f B Is a perfect matchi B Is a partial matchin a c e f g h

An airplane needs to head due north but there is a wind blowing from the northeast at 40 km hr The plane flies at an airspeed of 550 km hr To end up due north the pilot will need to fly the plane Select an answer of north Give your answer to the nearest tenth of a degree The resulting ground speed of the plane to the nearest kilometer per hour is km hr degrees

1 Find AC A 7 yd B 92 4 Find ZA 15 yd 75 28 B 28 yd 2 Find BC 15 5 Find Z B B 32 mi 28 A B 59 10 yd 21 mi 3 Find AC C B 83 6 Find Z C 38 25 m 98 19 ft 11 ft A B

in 13 of 13 Macmillan Learning The braconid wasp preys on the azuki bean weevil This predator prey relationship causes the wasp population to fluctuate The wasp population after t generations is given by w 3500 2000 sin After how many generations is the wasp population at a minimum for the first time Give your answer to the nearest whole number t What is that minimum number Give an exact answer minimum wasp population When is the first time the wasp population reaches 5400 Give your answer to the nearest whole number generation s generation s

A uniform strip of 5 cm wide frames a trapezoidal window as shown below Find the left dimension of the outside of the frame A 73 3 cm B 65 7 cm 81 6 cm 7 22 5 1 65 0 cm Fig 4 82 Str Copyright 2015 Pearson Canada Inc 5 0 cm

A supporting girder structure is shown below Find the length of x A 7 95 m B 7 23 m 7 56 m Fig 4 56 7 25 m 27 89 39 4 G Jhy UY Copyright 2015 Pearson Canada Inc 5 25 m

Let n t 7 Use a double angle formula to find sin 2t 8 Give an exact answer Use symbolic notation and fractions where needed 3 2 20 and sin t

45 Find the sine and cosine of 22 5 Note that 22 5 2 Give exact answers Use symbolic notation and fractions where needed Simplify your answers completely sin 22 5 cos 22 5 Now give the approximations of the obtained values Use decimal notation Give your answers to three decimal places sin 22 5 cos 22 5

Question 3 of 13 21 29 sin 1 and sin t Find sin 1 exactly Let both s and t be acute angles so that sin s 3 Give an exact answer Use symbolic notation and fractions where needed Now approximate the obtained value Use decimal notation Give your answers to three decimal places

e Find tan a B f Find the quadrant containing the angle a 3 Problem 5 Verify each identity a secx tan x sec x b tan 4x csc 4x cot 4x sec 4x C d sin t 6 sint 9 3 csc t 1 sint 3 csc t sect 1 cos t sec x sec t e f g sin x 2 sin x 1 cos x COS sin 0 cos 0 cos a B cos a B h tan sec 0 cos 0 0 1 sin x 1 sin x 1 tan a tan 3 1 tan a tan 3 1 tan 0 1 tan 0 Problem 6 If a person with weight W bends at the waist with a straight back then the force F in pounds exerte on the lowe back muscles may be approximated by the function F 3 2 89W sin 8 The ang B is the angle between a person s torso ard the horizontal a Use the sum and difference identities to rewrite the function F B in terms of cosine b Suppose the person is standing straight measure the force ororted on their book

oblem 4 Let tan a 2 3 and cos 3 3 where a is in the first Quadrant and is in the third Quadrant 3 a Sketch and complete a right angle triangle for the angle a b Sketch and complete a right angle triangle for the angle c Find sin a d Find cos a B e Find tan a f Find the quadrant containing the angle a

C A COS a Yanda verilen AB geninde AB AC dir 12 13 oldu una g re sin RAC de eri kart r

Next question 76 54 3 2 Give the equation of each line in the 5 graphs below Make sure to scroll down to see all the graphs Give your answers in slope intercept form unless the line is vertical 7 6 5 4 3 2 6 430 to 2 4 2 2 3 4 5 6 B 7 y 64 4 324 4 2 23 Y 456 Get a similar question 12 45 6 You can retry this question below D The equation of the line is y 5x X 6 7 The equation of the line is 5y syntax error this is not an equation X X

Problem 5 Verify each identity a secz tan sec r sec x b tan 4x csc 4x cot 4x sec 4x C d sin t 6 sint 9 sint 3 sect 1 1 cos t sect a p 3 csct 1 csc t e f g sin x 2 sin x 1 cos x sin 0 cos 0 sec 0 cos 0 cos a b cos a B h tan 0 1 sin x 1 sin 2 1 tan a tan 3 an B 1 tan a tan p 1 tan 0 1 tan 0