Trigonometric equations Questions and Answers

ometry Spring 2023 Sp23 MAT 2 Points DETAILS Consider the following Assignment 8 Analytic Trigonometr g x cos 2x 3 sin 2x a Express the function in terms of sine only g x

1 Points DETAILS Make the indicated trigonometric substitution in the given algebraic expression and simplify see Example 7 Assume that 0 0 7 2 1 x x tan e Need Help Read It MY NOTES 1 Points Make the indicated trigonometric substitution in the given algebraic expression and simplify see Example 7 Assume that 0 07 2 DETAILS MY NOTES

Simplify the trigonometric expression csc x cotx sin x 9 I Need Help Submit Answer 5 1 Points Read it DETAILS

Three mutually tangential circles A B and C have radii of 9 ft 10 ft and 11 ft respectively Part 1 of 3 a Find the area of AABC Round to the nearest tenth of a square foot The area is approximately 172 3 Part 1 3 Part 2 of 3 b Find the measures of angles A B and C Round to the nearest tenth of a degree m Ing

44 names are placed into a drawing Four names will be drawn The first name drawn wins a 100 gift card The second wins a 50 gift card The third wns a 30 gift card and the last name drawn wins 20 How many different ways can the winners be chosen

1 Points DETAILS Find the side labeled x Round your answer to one decimal place X X 52 69

Find all solutions of the given equation Enter your answers as a comma separated list Lt be any integer Round terms to two decimal places where appropriate 4 cos 8 1 0 0 Need Help Road 1 Points DETAILS SPRECALC7COREQ 7 4 034 Find all solutions of the given equation Enter your answers as a comma separated list Let it be any integer Round terms to two decimal places where appropriate 2 0 1 0 0 Need Help rad Submit Anwar Need Help rad Haad 1 Points DETAILS SPRECALC7COREQ 7 4 038 Find all solutions of the given equation Enter your answers as a comma separated list Let be any integer Round terms to two decimal places where appropriate 8 2 0 rad Road

a 2 1 Solve for 0 sin where a is a rational number 0 sin a 2 1 a 0 1

3 The following graph can be described using an equation of the form y Acos x C Determine the values of A and C Show how you arrived at your answers 2 9 2T 9 0 9 Oberwoll t sit to dors d W

For all i EN let f x y Sy 1 5x 1 5 If maps the rectangle 6 8 x 3 4 to 32 37 x 26 31 for some positive integer value of i enter that value of i If there is no such i instead enter i 1

Temperature T is transported by a combined steady convection and diffusion process through a one dimensional domain L with boundary conditions as shown T 400K The governing equation is x 0 T 300 U 100 UT dx dT exp T For U 2 0m s and I 0 3 m s using the upwind scheme to discritize the above equation for L 2 0 m using 6 equally spacing cells solve the algebra equations and compre your results with T 300k x L P 1 exp alls

The table below shows the results of a study assessing the prevalence of depression among 200 patients treated in a primary care setting using tw methods to determine the presence of depression one based on information provided by the individual i e proband and the other based on information provided by another informant e g the subject s family member or close friend about the proband Calculate the degree of agreement between the two approaches using the Kappa Contingency Coefficient K Proband Depressed Proband Not Depressed Total Depressed 65 19 21 Informant Not Depressed Total 115 85 200 50 66 116

At noon ship A is 50 nautical miles due west of ship B Ship A is sailing west at 23 knots and ship B is sailing north at 24 knots How fast in knots is the distance between the ships changing at 7 PM Note 1 knot is a speed of 1 nautical mile per hour Note Draw yourself a diagram which shows where the ships are at noon and where they are some time later on You will need to use geometry to work out a formula which tells you how far apart the ships are at time t and you will need to use distance velocity time to work out how far the ships have travelled after time t

Compute the coefficients of the Fourier series for the 2 periodic function f t 2 5 cos 2nt 9 sin 3mt By a 2 periodic function we mean a function that repeats with period 2 This means we re computing the Fourier series on the interval 1 1 ao a1 02 03 a4 b b b3 b help numbers

Find the reference angle for the angle 5 2 The angle is measured in radians not degrees The angle is Round to pogroot hundredth o ponded

1 678257 A ladder 25 feeting is leaning against the wall of a house The base of the ladder

17 Find a set of parametric equations for the conic section or the line below Ellipse Center 5 3 Vertices 6 units above and below the center Endpoints of Minor Axis 2 units left and right of center A x 5 2 cos t y 3 6 sin t B x 5 6 cost y 3 2 sin t C x 5 2 cost y 3 6 sin t D x 2 5 cost y 6 3 sin t

Find the exact value of the expression 2tan 105 1 tan 105 3 LC S QUESTION 32 Find the exact value of the expression without the use of a calculator 5cos 2sin 4 07 2 2 07 2 14 2 T 4

cos 1 tan 1 7x 0 12 7x 12 12 7 QUESTION 30 Find the exact value for the expression under the given condition sin a B sin a 0 5 24 2 39 0 5 24 2 39 12 10 2 39 12 10 2 30 12 for a in Quadrant IV cos for in Quadrant I 13

Use the given information to find the exact function value 1 Given sin and tan 0 find cos 20 O 79 781 8 5 9 O 79 81 8 5 9

A person goes up a set of stairs and boards the bottom of a ferris wheel At t 0 seconds the ferris wheel starting turning and the height of the rider above the ground in feet is given by h t 32 20 cos nt 45 a What is the radius of the ferris wheel feet b How long does the ferris wheel take to make one revolution 3 c When does the rider first reach a height of 27 feet Give your answer to the nearest second seconds at about seconds

Use the product to sum identities to rewrite the following expression as a sum or difference 3sin 3 sin 33

12 The Washington Monument in Washington D C is approximately 169 meters tall A camera is 65 meters from the base of the monument and is moving along the horizontal ground away from the monument while keeping the top of the monument in view What is the camera s horizontal velocity when the angle of elevation to the top of the monument is decreasing at 0 11 radians per second

Find the exact value COS 1 V2 2 COS 1 2

Find an angle between 0 and 2 that is coterminal to the given angle 17 4 TC 1 87 2 05 4 TC 1 4 T

aj a 40 0 2 b cot 90 0 tane 2 tan o 2 tan O cot 90 0 f sin 45 cos 45 1 false Sin 45 cos 45 cot 90 0 Sin 45 cos 45 2 11 2 2 2 Sen Cos 0 old 0212 COS 90 0 sen 90 0 s 913 J1 o b

Use the periodic properties of the trigonometric functions to simplify each expression to a single function of 0 cot 0 sec 0 2 csc 0 sin cos seco CSC tan cot

Part 1 of 2 a Write the solution set for the general solution Use n where n is an integer TC 2 the numbers using integers or simplified fract The solution set for the general solution is xx Part 1 2 Part 2 of 2 b Write the solution set on the interval 0 2 The solution set on the interval 0 2 is 2nt x 7 6 2nn

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Identify the amplitude period phase shift and vertical shift and graph the function f x 5sin 4x 2 Amplitude 5 T Period 2 Phase shift Vertical shift 2 84 AAAAA Amplitude 5 T Period 2 Phase shift Vertical shift 2 Iv

Find the value of the expression sin 135 cos 135 sec 30 csc 30 2 3 3 2 3 2 3 2 3

1 tan 8 sin a Special Angles exact value of each trigonometric function 2

For the following functions ii Identify the asymptotes and zeros if any Graph at least four periods with clear labels y sec 2x b y csc 3x

Question 7 Points 1 Choose the correct answer Laws that allow workers to work in a shop without having to join a union are called O antitrust laws Oright to work laws closed shop laws O AFL CIO laws

19 Ethan is flying a kite at an angle of 57 1 m above grou The kite and Ethan are 8 5 m apart along the ground ro At what height from the ground is the kite the flying b How long of a string is being pulled C At what angle is the string attached to the kite

5 Let 8 be an angle such that tan0 and esc00 12 Find the exact values of sine and sec 0 sine sece 8 X 9

Solve the given differential equation dQ dt t Q t In t

Find all solutions of the equation in the interval 0 2x Enter your answers as a comma separated list If there is no solution enter NO SOLUTION 9 sec x 9 tan x 9 Check which variable s should be in your answer Find the x intercepts of the graph Enter your answers as a comma separated list Use n as an arbitrary intege y 5 sin xx 5 cos x A 0 5 0 5 1 0 1 5 2 0 2 5

how did mathematics influence ancient greek architecture

Find the amplitude and period of each function Then sketch one cycle of the graph of each function Show all work including tables 24 y 3 sin 4x 27 y cos 0 n 2 28 y sin x 2 1 25 y 2 cos

Directions Fill out the blank unit circle below Try your best to practice this without looking at your key Then use the chrt to match the radions to the degree C L

Using only trig identities not the trig definitions x y r find the remaining five trig functions of a given the followin 33 sin 3 and cos 0 0 34 tan 02 and csc 0 0

1 point Let y f x be a periodic function whose values are given below Find the period amplitude and midline x 3 7 11 15 19 23 27 31 35 f x 13 11 4 13 11 4 13 11 4 a The period of the graph is b The midline of the graph is c The amplitude of the graph is help numbers help numbers help numbers

Use a numerical solver and Euler s method to obtain a four decimal approximation of the indicated value First use h 0 1 and then use h 0 05 y x y y 0 0 7 y 0 5 y 0 5 y 0 5 h 0 1 h 0 05

dy olve the given differential equation by using an appropriate substitution The DE is of the form dx dy dx sin x y f Ax By C

The lengths of a shadow cast by a gnomon a device used to tell time of heighth when the angle of the sun above the horizon is can be modeled by the equation h sin 90 0 0 0 90 sin 0 a Verify that sh cot 6 Simplify at each step h sin 90 6 sin 0 h cos 8 h cot 6 G b Use a graphing utility to create a table of the lengths s for different values of 9 Let h 4 feet Round your answers to two decimal places 15 30 45 60 75 sin 8 90 0 x x x x X S

Select the correct choice tan 15 25 2 25 2tan 15 25 2sin 15 25 2cos 15

For short 10 km distances you can find the distance between two points of lat and long with the equirectangular equations Look up the radius of the earth Re in meters x long2 longi cos lat2 lat 2 y lat lati d Re x y What is the percent difference between your two distance measurements di and d diff d d l d d x 100

A Ferris wheel is 10 meters in diameter and boarded from a platform that is 2 meters above the ground The six o clock position on the Ferris wheel is level with the loading platform The wheel completes 1 full revolution in 4 minutes How many minutes of the ride are spent higher than 10 meters above the ground

e number of hours H of daylight in Madrid as a function of date is approximated by the formula ere t is the number of days since the start of the year We can think of t 0 as the stroke of midnight on Dec 31 Jan 1 thus January falls between t 0 and t 31 February falls between t 31 dt 59 etc nd the average number of hours of daylight in Madrid assuming in each case that it is not a leap year in February average hours in July average hours H 12 2 4 sin 0 0172 80 over a year average hours