Trigonometric equations Questions and Answers

The graph of y f x is shown below b Does lim f x exist x 1 CYes No c Doesf Answer each of the following questions about f x You have one submission for each question a Does lim f x exist x 1 Yes No fix exist Yes No From left to right the graph is a horizontal line to a hollow point at 1 1 Then the graph jumps to a filled in point at 1 3 and continues to the right as a horizontal line c is fix continuous at x 1 CYes No 1 e Is x differentiable at x 1 CYND 2 3

Given the Fourier transform A t sinc f the Fourier transform of the signal in the figure is 01 Xb f j2sinc f 1 j2sinc f 1 2 X f 0 5j sinc f 1 0 5j sinc f 1 03 X f j4nfsinc f sinc 2f O 4 None of the answers 05 Xb f j0 5fsinc f sin 2 f x 1 0 2

Which of the following values of the correlation r indicates the strongest correlation between the two variables a r 1 22 O b 0 75 O c 1 22 O d 0 81 O e 1 9

d lim x tanxe 20 24 Sing

Construct an appropriate triangle to complete the table 0 8 90 0 0 x 2 deg 8 rad Function Value Function sin 6

21 Solve AABC given AB 35 cm BC 19 cm and ZA 30 Round all angles and sides to 1 decimal place

Question 2 f 3dx 1 Select one a In 6 b 3ln 3 In 8 d ln 2 C Not yet a Marked o

cos 3x 10 cos 2x denkleminin A 2 0 180 aral nda ka farkl k k vard r B 3 C 4 D 5 E 6

Core 0 60 0 6 answered Question 4 Simplify sin x 7 to a single trig function using a sum or difference of angles identity Question Help Video 1 Video 2 0 10 pt

Question 7 Simplify to an expression involving a single trigonometric function with no fractions sin x cot a cos x 0 10 F

0 10 pts 399 Details sin Evaluate the expression cos

0 10 pts 399 Details Use your calculator to evaluate cos 0 22 to at least 3 decimal places Give the answer in radians

9 Alex kicked a soccer ball from the ground to Dzeps standing 30 ft away If the maximum height the ball reached was 12ft write a quadratic equation to model the path of the ball written in factored form factored form g a x p x

Strategies used by entrepreneurs to overcome barriers to entry do NUI include O combatting customer lock in O finding ways to reduce costs O using regulatory strategies to the entrepreneur s advantage

Using DeMoivre s theorem find 4 2j 5 KIL This question 3 point s 4 25 cos cos isin 0 Simplify your answers Round to two decimal places as needed Type any angle measures in degrees Use angle measures greater than or equal to 0

Suppose cos x and 90 x 180 a 5 pts Use identities to find the exact value of sin 2x b 5 pts Use identities to find the exact value of cos 2x c 5 pts In what quadrant is the angle 2x Explain your answer

If the nominal rate is 9 annually compounded continuously what is the effective rate O a 9 O b 9 211 O c 9 417 O d 9 678

11 6 pts Isabella went up and down the street to find out how many parking spaces each house has Find the mean median mode midrange and range of her results Here are her results Parking Spaces 1 2 3 Frequency 15 27 8

Find all solutions in the interval 0 2 2 sin 2x sinx cos x 0 GIZZB X Type an exact answer using a as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression

Problem 3 a and y are angles in quadrants 1 2 and 3 respectively such that tan a tan B COS Y This time we also that 27 a y 47 Evaluate the following a b c d b COS c tan sin sec 2 sqrt 2 4 sin 9 COS tan 2 0 2 Problem 4 0 is an angle in quadrant 3 such that 0 and such that cos 0 a sqrt 7 sqrt 5 14 5 02 0 3 2 Calculate the following

Solve the given trigonometric equation analytically Use values of x for 0 x 2 64 cos x 16 0 X radians Simplify your answer Type an exact answer using as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a comma to sepa

ations Question 5 of 10 What is the analytical solution Solve the given trigonometric equation analytically and by use of a calculator Compare results Use values of x for 0 x 2 2 cos x cosx 1 This quiz 30 point s possible This question 3 point s possi X Type an exact answer using as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression What is the solution using a calculator Round to two decimal places as needed Use comma to separate answers as needed

ations Question 10 of 10 This quiz 30 point s possible This question 1 point s possible Solve the following trignometric equation analytically and by use of a graphing calculator Compare the results Use values of x for 0 x 2 2 sin 2x cosxsin x 0 GILD Type an exact answer using zas needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your

Solve the given trigonometric equation analytically Use values of x for 0 x 2 16 sin x 4 0 nus possible This question 3 point s possible x radians Simplify your answer Type an exact answer using a as needed Type your answer in radians Use integers or fractions for any numbers in the expression Use a com

Write the parametric equations in the given Cartesian form Y x 2 sin 0 y 8 cos 0 with 0 x 2

Problem 1 Use the Law of Sines of the Law of Cosines when it applies Solve each triangle and assume standa labeling a b 3 4 c 2 8 A 82 b A 30 a 20 B 45 c A 30 a 5 b 5 2 d a 19 b 2 c 3 e a 40 2 A 135 B 30 f A 63 C 55 a 8 3 Problem 2 An airplane flies in the triangular course shown in the figure below C 300 mi

csct 1 hoose the sequence of steps below that verifies the identity csc t 1 cott csct 1 A cott cott csct 1 B C D csc t 1 csct 1 cott cott csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 cott csct 1 csct 1 cott csct 1 csct 1 csct 1 cott csct 1 csct 1 csct 1 csct 1 csc t 1 cott csct 1 csc t 1 cott csct 1 csc t 1 cott csct 1 cot t cott csct 1 cot t cott csct 1 cot t cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott cot cott csct 1 csct 1

antities Prove the given identity sin xsec x cos xcsc x sec xcsc x Choose the correct proof below OA sin xsec x cos xcsc x sin X cos x sin x cos x cos2x sinx cos sin x cos x sec Xcsc X OC sin xsec x cos xcsc x 1 sin x cos x sin x cos x cos x sin 2x cos2x x sin x cos x 1 sec Xcsc X sin x Question 7 of 10 This quiz 20 point s poss This question 2 point s pr OB sin xsec x cos xcsc x sin X cos X 2 sin x cos x sin x cos x 1 sin x cos x sec Xcsc X OD sin xsec x cos xcsc x sin x 2 sin x cos sin xcos X 1 cos x cos X cos2 sin x cos X sec xcsc x 1 sin x

112 In a recent sample of 84 used car sales costs the sample mean was 6 425 with a standard deviation of 3 156 Assume the underlying distribution is approximately normal a Which distribution should you use for this problem Explain your choice b Define the random variable X in words c Construct a 95 percent confidence interval for the population mean cost of a used car i State the confidence interval ii Sketch the graph iii Calculate the error bound al moons for this study

If f x and g x are arbitrary polynomials of degree at most 1 then the mapping f g f 2 g 2 f 2 g 2 defines an inner product in P Use this inner product to find f g f g l and the angle afg between f x and g x for f x 4x 8 and g x 4x f g f g afg Note X radians

of 13 In every Major League Baseball field the bases form a square with sides of length 90 feet In Fenway Park the distance from home plate to the fence at straight away center is about 410 feet The center fielder catches the ball with his back against the fence at this point He wants to make a play at third base See the figure How far does he have to throw the ball Home 90 90 distance Third base 410 Center field fence Give your answer to the nearest whole number feet

A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 12 in and period 0 25 seconds Its displacement d from sea level at time t 0 seconds is 0 in and initially it moves downward Note that downward is the negative direction Give the equation modeling the displacement d as a function of time t d 0 B 00 sin cos

nd value s for b such that the triangle has one solution two solutions and no solution A 84 a 325 6 a one solution Obs 325 6 or b 325 6 sin 84 Obs 325 6 O b 325 6 or b Ob 325 6 sin 84 Obs 325 6 or b 325 6 cos 84 b two solutions O 325 6 b cos 84 325 6 O 325 6 b O 325 6 b O 325 6 b O 325 6 b c no solution Ob 325 6 sin 84 Ob z 325 6 Ob 325 6 Ob 325 6 sin 84 sin 84 325 6 325 6 sin 849 325 6 sin 84 325 6 cos 84 06 275 on h 325 6

Write the equation of a sine or cosine function to describe the graph 3x m C 3x til 3 t 2 9x 3x 15 0

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 4002 1224 cos In this equation p t represents the total population size and f is the time in years Suppose we start at 1 0 years During the first 9 years when will the population size be 4700 Do not round any intermediate computations and round your answer s to the nearest hundredth of a year If there is more than one answer enter additional answers with the or button t 7 years or O

3 a Fi 2 cos x sin x 1

3 tan 1 0

8 Calculate the following using the Unit Circle and trigonometric identities of your choice Show all work and explain your reasoning for your solution Write exact answers i e no decimal solutions A cos 5 12 B sin 17 12 C tan 10 3

Min Compare the image above to the image below showing a fully contracted sarcomere hen 3 a Find all solutions of the following equations 2 cos x sinx 1 ANSWER b 3 tan 3 1 Heone ANSWER 1 0

9 of 13 Find all solutions of cos x 1 on the interval 2T 0 2 Give your answer in the form of a comma separated list if needed Express numbers in exact form Use symb fractions where needed X

on 1 of 13 Macmillan Learning Find all solutions of the trigonometric equation in terms of integer k and the solutions in a single period x Express your answer in radians 2 cos t 1 Give your answer in the form of a comma separated list if needed Express numbers in exact form Use symbolic notation and fractions where needed Use k to represent any integer

Find the value of x for the triangle shown below A 4 6 B 4 2 5 1 5 4 25 12

No late submissions will be accepted Problem 1 For each function find the amplitude range period phase shift vertical shift and a sketch including a full period a f t sin t t 1 3 2 7 b f x 4 cos 2x 1 Problem 2 The graph below models the monthly average precipitation in inches at a town on a particular mountain

2 Find the exact value of each trigonometric expression a cos sin n sin 3 b tan sin

7 If it is known that sin a 13 0 a 1 and that cos 2 5 value of sin a B 37 2 B 2 find the exact

9 of 13 Use a product to sum formula together with the knowledge of special angles to calculate the value of cos 54 sin 4 24 24 Give an exact answer Use symbolic notation and fractions where needed Simplify your answer completely s 54 sin 24 COS P

O Macmillan Learning Complete the passage to determine whether the function f t sin t cos t is even or odd Therefore the function is

Given a railroad curve with the following parameters D 2 00 00 18 00 00 PI Station 25 50 00 ft Compute the curve parameters the station PT O 34 78 12 O 47 69 42 O 65 43 21

Given a railroad curve with the following parameters Dc 18 00 00 2 00 00 PI Station 25 50 00 ft Compute the curve parameters the stations of the PC O 20 96 24 O 32 15 42 O 30 42 35

Problem 4 If the angle of elevation is 42 what is the length of a shadow on the level ground of a man who is 6 1 ft tall Include a diagram