Trigonometric equations Questions and Answers

Macmillan Learn In a certain right triangle the side opposite one of the acute angles t is five times as long as the adjacent side Find the sine cosine and tangent of t Express numbers in exact form Use symbolic notation and fractions where needed sin t cos t ton

Question 3 Suppose that p t is such that the Wronskian of any two solu tions of the equation 1 d y dt p t dy dt is also a solution Furthermore suppose that p 1 0 a 10 points Find p t 0 t 0 1

O Macmillan Learning In the given figure trigonometric points corresponding to compass points and special angles are marked Match the given angles with the appropriate points labeled in the figure X 3K 2 3n 4 radians radians 210 Answer Bank T 3 radians 30 315 radians 240

4 is 2 A 9 5 4 3 2 1 1 2 3 4 5 2 Identify the function whose graph appears above as f x a tan bx or f x a cot b x m A

2 In the following cases express the f t as a single sinusoid a f t cos wot 3 sin wot 5 points b f t 3 cos wat 4 sin wot 5 points

5 What are the amplitude and period of y 2 sin x 6 What is the average rate of change of the function y 3 sin 2x on the interval 0 12

Ferris wheel on a coordinate plane The center of the Ferris wheel is at the origin and one car lies on the x axis at 125 0 5 Construct a graph that relates the amount of time the car is in motion from 0 to 40 seconds to the height of the car with respect to the center of the Ferris wheel Describe the steps you took to make your graph 6 From your graph what are the amplitude frequency and midline Write the equation describing the relationship you graphed Explain 7 From your graph and its equation what is the average rate of change of a car from 0 to 5 r What does the rato can in this coptout Ch

1 2 points Show that the curve given by r t 1 2tt 3t 4t 1 lies entirely within a single plane and find an equation for that plane

10 If 2 sin 6 cos 6 cos 0 sin 6 03 02 1 1 then the value of cot is

Let y Find dy da tan x O sec x 2 tan x sec x O2sec x O2 tan x

3 If we simplififed cos A B cos A B we get Sellect all the correct options 2sin A sin B 2cos A cos B cos A cos B sin A sin B cos A cos B sin A sin B cos A cos B sin A sin B cos A cos B sin A sin B

1 Look at the right angled triangle below All the side lengths are shown on the figure A 5 5 4 C None of the other options is correct 3 Select all correct statements to find sine cosine and tangent of angle A sin A cos A sin A cos 4 tan A tan A B

i The weights in kg of 10 students are given below 29 33 26 28 36 41 23 34 34 33 Work out the median show you work

Bernoulli Equations The equation dy dx 2y xy is an example of a Bernoulli equation 1 Show that the substitution v y reduces equation 1 to the equation dv dt 2 Solve equation 2 for v Then make the substitution v y to obtain the solution to equation 6v 3x

Change 527 to base eight

Solve the given initial value problem y x x 3 dx y In x y 1 25 x ln x 3x ln x 2x 3x 207 2 x 3 X Give the largest interval I over which the solution is defined Enter your answer using interval no 1 0 00

Perform the multiplication and express the answer in scientific notation Choose the correct answer 6 x 105 x 0 5 x 10 3 x 107 6 5 x 107 O 3 x 10 0 6 5 x 10 0

12 Which one of the following examples represents a proper fraction O A 15 22 O B O C 3 O D 12

P cos 30 0 25 200 Psin 30 62 118

What is the range of the data 2 3 4 5 6 7 1 1 11 6 O O 5 3 O 6 7 10 6 4 5 11 7 8 5 3 2 6 7 7 9

Determine the equilibrium constant for the following reaction at 549 K CH2O g 2 H2 g CH4 g H2O g AH 94 9 kJ AS 224 2 J K O 2 08 10 3 O 1 07 x 109 O481 O 1 94 x 10 12 O 9 35 10 10

2 A regular hexagon on the pseudosphere H is inscribed in a c cosh r 3 Find the exact value of cosh s where s is the length of ea Please do not use a calculator Please fully justify your answer

The figure shows two right triangles That is angles CAO and BCO are right angles You may assume the following side lengths AC 20 BC 20 and AO 13 Determine angle ADB in radians Decimal approximations will be marked incorrect Symbolic trigonometric expressions such as arctan 5 are accepte B A05 x radians C A

The Spice of Life Restaurant Supplies has experienced growing sales and management is looking to expand They currently own a lot near Ponce City Market Management plans to do a marketing survey in the future to investigate whether it is a good location The survey cost will be 10 000 The lot was purchased two years ago at a cost of 1 500 000 Today the property could be sold for 2 000 000 because of the increase in real estate prices The land will have to be cleared at a cost of 40 000 The company can then construct a new building at an estimated cost of 3 200 000 including landscaping and parking Finally management will hire a new manager for the location with a salary of 100 000 What is the cost of this expansion project 5 350 000 4 850 000 4 750 000 5 340 000

Find the right part of the identity tan cot O sin e O sin cos 8 O sec 9 O cs A CSC

The curve above is the graph of a sinusoidal function It goes through the points 9 0 and 5 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 please explain f x

Sketch the graph of the given function Check your answer using a graphing calculator y 3 sin 12x Choose the correct graph below OA 41 160 12 126 A Q OB O C Q O D

The bearing from A to C is S 55 E The bearing from A to B is N 84 E The bearing from B to C is S 35 W A plane flying at 250 mph takes 2 3 hr to go from A to B Find the distance from A to C The distance from A to C is mi Round to the nearest integer as needed

The cost function for a certain commodity is C q 86 0 14q 0 007q 0 0005q a Find C 100 100 X Interpret C 100 This is the amount of time in minutes it takes to produce 100 items This is the rate at which the production level is decreasing with respect to the cost when x 100 This is the number of items that must be produced before the costs reach 100 This is the cost of making 100 items This is the rate at which costs are increasing with respect to the production level when x 100 b Find the actual cost of manufacturing the 101st item Round your answer to the nearest cent 11 3054 x x Enhanced Feedback Please try again For part a find the derivative of C and evaluate it for the given value For part b the cost of the nth item is C

46 45 44 43 y us 7 8 7 6 5 4 2 2 5 3 4 15 6 Write an equation for the function graphed above

6 5 4 3 2 1 8 7 6 5 4 3 2 7 2 3 4 15 60 8 1 2 3 4 5 Write an equation for the graph above f x 6

6 sec sin 2 giver cos 2 and 73 3 sin 0 In what quadrant does 23 terminate 5

J F nds where F x y i y z j xy y k Use Gausss theorem to evaluate and is the closed surface formed by the cone z 2 4x y in the first octant y2 and the hemisphe

9 Find the exact value of the indicated trigonometric function of 0 given that sec 8 8 Find tan 0 17 8 Question Viewer and 0 is in quadrant IV

Determine the amplitude period and displacement of the given function Then sketch the graph of the function y 2cos The amplitude is The period is The displacement is Type an exact answer using a as needed Use integers or fractions for and numbers in the expression Choose the correct graph OA 2x Q G B Q 5 O C Q D Q E

0 2 For 13 15 Solve Algebraically for Interval 0 2T 13 Cos 3x cos2x COS X 0 14 sinZa cosa 0 15 2tan 2x 3 6

Problem 7 18 pts Estimate the value of the following integral using n 4 in each case Round answers to six decimal places 1 cos x dx n 4 a Trapezoidal Rule

mula for the number of permutations of n distinct items is n

Select the appropriate qution that under the graph 19

The amount of a drug in milligrams in a patient s bloodstream is given by the equation y 6 0 4x where x is the number of hours after the drug is administered given to the patient After how many hours will the amount of drug in the bloodstream reach 0 mg 15 hours 6 hours cannot be determined 0066 ho

Question Use a power reducing formula to simplify 20cos4 x Write your answer as an equivalent expression that does not any powers of sine or cosine greater than 1 Note When entering your answer put parenthesis in with cosine e g cos 4x

A cross section of a tunnel is parabolic The tunnel is 25 feet high in the middle and the tunnel is 30 feet wide a Can a semi truck that is 14 feet tall and 10 feet wide pass through the tunnel in its ow lane if there is a two lane road going through the tunnel Enter yes or no b What is the height of the tunnel at the potential problem spot feet Round to the nearest tenth

6 Given the trigonometric function y 3sin x 60 1 Draw a sketch then graph A 5 I I 1 1

Solve the right triangle with A 62 3 and B 27 7 Round off the results according to the table below Measurements of Angle to Nearest 1 0 1 0 01 Accuracy of Trigonometric Function 2 significant digits 3 significant digits 4 significant digits KITE Select the correct answer below and if necessary fill in the answer boxes to complete your choice SOA a OB There is not enough information to solve the triangle Points 0 of B

19 Sketch the function h x 4 cos 2 x 30 Include an appropriate scale on both axes

31 Sketch one cycle of the graph of y 3 sin x 90 Include an appropriate scale on each axis K

e g 10 Solve AABC given that A 62 a 14 2 inches and b 12 9 inches

From Unit 4 Lesson 7 7 Technology required What is the value of x 3 40 F X 50 E

Find f x for the given function Then find f 4 f 0 and f 2 f x 14 x f 0 1

1 The forward difference formula can be expressed as h xo xo h xo ro 0 h Use Richardson extrapolation to derive an O h formula for f ro In addition obtain a table similar to the one appearing at the end of Lecture Note 15 EXAMPLE 6 5 Extrapolating the Derivative of the Natural Logarithm Let s reconsider the approximation of the derivative of the function f x Inx using the second order central difference approximation formula With xo 2 we ind h 0 1 0 05 0 025 Dh f zo h f zo h Error 2h 0 500417292 0 500104205 0 500026043 h 0 1 0 05 4 17 x 10 4 1 04 x 10 4 2 60 x10 5 Applying the extrapolation formula to these results produces 4Dh 2 Dh 3 Error 0 499999842 1 58 x 10 7 0 499999989 1 10 x10 8 Not only has the approximation error been significantly reduced as a result of extrapolation the cut in error due to the cut in the step size is also larger In par iouler it onnoers on if the extrapolated values are fourth order opproximations