Trigonometric equations Questions and Answers

12 1 point Which tool or strategy could you use to solve the triangle 16 mm the cosine ratio the cosine law 11 mm b C the sine law d There is not enough information to solve this triangle

Solve the following initial value problem y 2y 17y 180e x y 0 35 y 0 13 y 0 11 y x

Let csc 0 7 and cot 0 0 Use fundamental identities to find the exact values of the trigonometric functions for the given conditions sin 0 csc 0 cos 0 secA tan 8

Given y sin x 7 2 1 Given y c Amplitude c Increments

2 The point 3 7 lies on the terminal arm for angle 0 Determine the primary and reciprocal trigonometric ratios for angle 0 3

12 Which graph represents the trigonometric function f 0 sin AMA O O O H 7 BEG

Sketch an angle 8 in standard position such that has the least possible positive measure and the point 14 2 is on the terminal side of 0 Find the values of the six trigonometric functions for the angle Do not use a calculator Sketch an angle 8 in standard position such that has the least possible positive measure and the point 14 2 is on the terminal side of 0 Choose the correct graph below O A Ay Q OB CALLE Q O C O D

Any offset between a stationary radar gun and a moving target creates a cosine effect that reduces the radar reading by the cosine of the angle between the gun and the vehicle That is the radar speed reading is the product of the actual speed and the cosine of the angle Find the radar readings to the nearest hundredth for Auto and Auto B shown in the figure Auto A 9 angle Actual speed 58 mph The radar reading for Auto A is mph Auto B Radar gun 18 angle Actual speed 58 mph

rmine the largest interval a b for which Theorem 1 guarantees the existence of a unique solution on a b to the initial value problem below x 49 y exy In x y 6 1 y 6 0

10pt A person is standing on the ground and looking up at a statue that is 130 feet tall The person is 240 feet away from the statue What is the angle of depression from the top of the statue to the person Round your answer to the nearest tenth

A hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 14 and 17 How high in feet is the ballon

Use the Pythagorean Theorem to determine the length of the hypotenuse BC Give the value for each trigonometric ratio using exact form Do not use decimal approximations sin B cos B tan B sec B csc B cot B 7 Remember that opposite and adjacent legs depend on which angle you re looking at Use SOHCAHTOA if you re having trouble remembering

Use a graphing utility to approximate the solutions to three decimal places of the equation in the interval 0 2 Enter your answers as a comma separated list 8 cos x cot x 8 8 sin x 3

Prove the identity 1 1 cosx 1 1 cosx 2csc 2x

Include all answers with comma betweer Solve the following quadratic equation using the quadratic formula 4 b b 4ac 2a x 15x 56 0

If f 0 tan 0 7 find f 0 f 0 x Simplify your answer

T 111 N 3 b LLL Absolutbeloppet i c n got r fel Let y be the unit circle z 1 with the usual counterclockwise orientation Evaluate the following integrals for m 0 1 2 m a z dz b z dz c Sz dz K Solution Set z e where 0 0 2 and thus dz ie de a c 2 z dz e m ie d i eime 0 C2 zmdx for e m ic 7 0 e imei ie do i ei m 1 de 1 m 1 2 if ei 1 m de 0 ei2 m 1 1 2 ei m 1 07 m 1 0 0 2 i e 1 m 07 1 t m m e 2x m 1 1 1 0 m 1 m 1 m 1 2 i m 1 2 2 eimo 1 S 2 d 10 0 2 1 0 0 zm dz eime de m 2 m 1 im im 0 0

Now consider k 1 Enter your final answer a comma separated list 72 3 52 3x 72 5x 13x 4 12 W 8x 7 12 12 812 5m 13m 12 Step 3 Finally do the same calculation for k 2 For greater values of k you will be outside the interval Enter y final answer as a comma separated list 12 3 2 5 2 x 87 12 12 X 8m Now state all solutions in the interval 0 2x Enter your answers as a comma separated list

Without a calculator find two solutions 0 0 360 that make each of the following equations true tane 1

O Macmillan Learning Suppose the country of Lilliput exported 241 billion worth of goods and imported 445 billion worth of goods in the last calendar year a Calculate Lilliput s balance of trade b Which type of trade balance is Lilliput running a trade deficit O neither a trade deficit nor a trade surplus O a trade surplus billion

1 8 points Suppose that Jim hit a golf ball with an initial velocity of 150 feet per second at an angle of 30 to the horizontal The position of the ball as a function of time can be described with the following parametric equations x 75 3t y 16t 75t a How long was the golf call in the air b When was the ball at its maximum height c Determine the maximum height of the ball Round to 2 decimal places d Determine the distance that the ball traveled how far away it landed Round to 2 decima

Convert each polar equation to rectangular form a r sin 0 3 Rectangular form y xi b r 8 2 Rectangular form 64 x y X 8 0 0

Problem 2 10 Consider the following right triangle If AB has length 4 find a the length of AC b the length of BC

Find the equation of the ellipse passing through the points 2 2 and 1 sqrt 6 and its center is at the origin 0 0

Establish the identity COS cos x X tan 1 tan 1

a Solve the equation tan 0 20 2 for 360 0 360 giving your answers to the nearest degree b Find the exact values of x in the interval 0 x 360 for which 3 tanz 2 cos

Use the accompanying histogram to answer the following questions a How many homes were included in the survey b In how many homes were five televisions observed c What is the modal class d How many televisions were observed e Construct a frequency distribution from this histogram a There were 31 homes included in the survey Type a whole number homes where five televisions were observed b There were Type a whole number Number of Homes ONFOOS Televisions per Home 2 4 Number of Televisions

Find the quotient N Z 5 5i Z Z of the complex numbers Leave your answer in polar form Z2 Z 1 i

Use DeMoivre s Theorem to find the indicated power of the complex number Write the answer in rectangular form 4 cos 105 i sin 105 4 cos 105 i sin 105 Simplify your answer including any radicals Type your answer in the form a bi Use integers or fractions for any numbers in the expression Rationalize the denominator

Find the Fourier series of f on the given interval fo n x 0 2x OSX f x 00 Give the number to which the Fourier series converges at a point of discontinuity of f If fis continuous on the given interval enter f x

The forces F F2 F3 Fn acting on an object are in equilibrium if the resultant force is the zero vector F F2 F3 F 0 The forces shown in the graph on the right are acting on an object a Find the resultant force b What additional force is required for the given forces to be in equilibrium 8 a The resultant force is Simplify your answer Type your answer in terms of i and j 8 y 4 8 FFI 00 3 X

Calculate the x and y components of the vector given below Do not round any intermediate computations and round your responses to the nearest hundredth 50 87 43 50 X y

Calculate the given quantity if a i j 5k b 31 5j k c j 4k a 2a 3b b lal c a b d ab e bx cl f a bxc 9 the angle between a and b rounded to the nearest degree

Solve each trigonometric equation in the interval 0 2x rounded to two decimal places Enter your answers as a comma separated list a 8 sin 8 1 0 8 b 8 c 8 d 8 2 cos 8 1 sin 8 1 0 2 cos 9 3 cos 0 2 0 sin 29 cos 9 0

68 DETAILS a Graph the polar equation r 8 cos 0 10 15 10 5 10 5 10 15 10 5 3 10 15 5 5 10 10 X 15 10 10 5 5 10 3 51 10 y 10 5 10 5 X 10 10 X What type of curve is this The graph of the polar equation consists of all points on the circle with radius 8 and center 4 0 The graph of the polar equation becomes a horizontal line at y 8 The graph of the polar equation consists of all points on the circle with radius 4 and center 4 0 The graph of the polar equation becomes a vertical line at x 8 The graph of the polar equation consists of all points on the circle with radius 4 and center 0 4 b Convert the equation to rectangular coordinates

Sine Graphs Which equation would have a graph with a period of with y sin x x 4 y sin 2 x 4 y x sin x y sin x 1 2 O Question 8 8 33 points Sine Graphs Which equation below has an vertical shift of 2

Sine Graphs Determine a possible equation of the following sine graph 2x 3x S Oy mx Oy sin x 1 Ox x y sin x St 4 V sin X K 4 w D GIN Kisht SM 4 124 NRI 2 3 M S 3 7 2x 4

Basic Trigonometry A school located due south of a park is 2 6 miles due east of a lake as shown in the map Which expression represents the distance between the lake and the park 2 6 cos 400 miles 2 6 tan 400 miles 2 6 tan 40 miles 2 6 cos 400 miles Lake 40 2 6 miles Park Schoo

In physics lab Ellie attaches a wireless sensor to one of the spokes of a bicycle wheel spinning freely on its axle The graph below shows the sensor s height above the ground in centimeters over time t measured in seconds Sensor s height in cm 50 40 30 20 10 y 0 1 2 75 48 7 25 38 2 3 4 5 6 11 75 48 16 25 38 7 8 9 10 11 12 13 14 15 16 Time in seconds Write an equation in terms of y height in centimeters above the ground and t time in seconds to represent the given context 17 18 t

Plot the point that has the given polar coordinates 6 72 2 2 x 2 R 2 0 0

4 Solve for x sin 2x 2 sin x 2 cos x 2 T4 marks

3 Prove the following trigonometric identities A 4 marks 1 cscx cotx secx tan x

What is exact value of csc 300 O O 3 2 3 2 O 2 01 13 3 O 2

Suppose that Miguel s blood pressure can be modeled by the following function p t 96 23 sin 124nt Miguel s blood pressure increases each time his heart beats and it decreases as his heart rests in between beats In this equation p t is the blood pressure in mmHg millimeters of mercury and t is the time in minutes Find the following If necessary round to the nearest hundredth Number of heartbeats per minute Time for one full cycle of p minutes Minimum blood pressure mmHg X

Find the reference angle for radians wwwww 8 5 0 0

e a cofunction to write an expression equal to csc CSC T 0 100 8 A sin cos 0 SA

A written discussion of both the similarities and differences between people objects or ideas is called a compare and contrast essay O an analysis a working thesis a cause and effect essay

A sine function has a phase shift of 60 to the right and a vertical translation of 2 units down What is a possible equation for this function O a y sin x 60 2 Ob y sin x 60 2 O c y sin x 60 2 600 2

Evaluate the function for the given value f x e x 3 f 3 Type an integer or THEE decimal Round to the nearest thousandth

sin x sin y cosx cos y O A Which of the choices shows the key steps that can be used to verify the identity x y x y 2 x y 2 2 cos x cos y OB cot O C sin x sin y cos x cos y sin x siny cosx cos y sin x sin y cos x cos y x y 2 2 sin 2 sin COS x y 2 cos x cos y 2 sin COS x y 2 x y 2 cos x cos y COS x y 2 2 sin 2 sin 2 sin x y 2 2 sin 2 sin x y 2 2 cos COS x y 2 x y 2 x y 2 sin COS sin COS x y 2 x y 2 x y 2 x y 2 x y 2 COS cot cot x y 2 x y 2 x y 2 cot x y 2