Algebra Questions

8 Sketch the graph of the function below being sure to include at least two full periods y sin 2x T y

1 4 A weight is oscillating on the end of a spring see figure The position of the weight relative to the point of equilibrium is given by y 12 displacement in meters and t is the time in seconds Find the times when the weight is at the point of equilibrium y 0 for 0 t 1 Equilibrium www cos7t 3sin 7t where y is

13 Use a graphing utility to graph the function f x 1 1 2 sin r cos2x

8 Sketch the graph of the function below being sure to include at least two full periods sin 2x 7 y

27 Find the reference angle 0 5 7 O 0 2 5 7 O 0 5 7 O 0 5 7 2 O 0 5 7 O 0 2 5 7

26 Given sin 30 tan 30 O tan 30 3 O 3 3 tan 30 O undefined O tan 30 200 2 1123 and cos 30 3 2 determine the following

21 Solve the following equation 2sin x 6cos x O 1 O O 4T 3 n O n n 2 T 3 2 2 1 1 O 3 n n 2 T 3 n 2 t 5 n 2 T 3 n n n

O O O O 23 Find the point x y on the unit circle that corresponds to the real number t t t t t t 25 3 25 3 corresponds to the point 25 25 1 3 25 3 O 25 t 3 corresponds to the point corresponds to the point corresponds to the point corresponds to the point 1 1 12 5 1 3 1 1 3 2

20 The angle of elevation of the sun is 33 Find the length 1 of a shadow cast by a tree that is 35 feet tall Round your answer to two decimal places O 1 39 82 feet O 1 53 90 feet O 1 41 73 feet O 1 53 30 feet 1 64 26 feet

O 9 Find if possible the complement of the following angle I 5 Complement Complement Complement 5 3 TT 3 3 TT Complement 10

3 sin cos 12 sin pro O6 6cos O 6 6 cos I O 6 sin 12 06 6 sin 12 I 12 6 cos os J 6 um for a to white the give as a sum of

O 3 Find all solutions of the following equation in the interval 0 27 sin x 3 TT 3 cosx 3 5 TT 4 O 5 7 5 0 4 50 5 TT 01 11 2

11 Find the exact value of the given expression 2 5T 3 sin O 3 1 2 2 O 3 1 2 2 O 3 1 2 2 O 3 1 2 2

12 2 Determine the quadrant in which an angle 0 lies if 11 1st quadrant O 4th quadrant 2nd quadrant 3rd quadrant

12 Find the area of the triangle having the indicated angle and sides B 123 a 64 c 28 Round your answer to one decimal place O 753 4 O 751 4 O 1 502 9 O 750 4

10 Consider the function given by y x 5cosx Use a graphing utility to select the graph of the function

5 Write the given expression as the cosine of an angle cos 60 cos 25 sin 60 sin 25 O cos 60 O cos 35 cos 85 cos 25 cos 50

The power dissipated in an electric circuit is given by the expression P RI2 where R is the resistance of the circuit and I is the current through the circuit For a sinusoidal alternating current the current might be represented by the relation I A sin 27ft where A is the amplitude f is the frequency and t is time Write an expression for P involving the sine function and use a fundamental identity to write P in terms of the cosine function OPRA sin 2 ft P RA RA cos 2 ft OP RA sin 2 ft P RA cos 2 ft OPRA sin 2 ft P RA cos 2nft P RA sin 2 ft P RA RA cos 2uft

1 Let w be a vector with initial point 4 4 and terminal point 2 5 Write w as a linear combination of the standard unit vectors i and Ow 6i 9j Ow 8i 3j Ow 0i 3j Ow i 6j w 2i 9j

T X 14 Find the reference angle and sketch and in standard position 0 155

a Use rotation of axes to show that the following equation represents a parabola Write the equation in XY coordinates Use a rotation angle that satisfies 0 y 2 and that eliminates the xy term 2 2 x y 7x 9y X Find the XY and xy coordinates of the vertex and focus vertex focus x coordinates x y XY coordinates Your answer cannot be understood or graded More Information Find the equation of the directrix in XY and xy coordinates Y coordinates X xy coordinates x y x y

X 5 Describe the behavior of the function below as x approaches f x 3 cotx O f 1 as x O f as x O f 1 as x n O O f o as x T f 0 as x T

X 15 The point 8 15 is on the terminal side of an angle in standard position Determine the exact value of cot 0 17 15 O cot e cot 8 cot 0 cot 8 cot 8 15 17 15 17 15 8 15

X 18 Use the formula asin BO bcos B0 a b cos B0 C where C arctan a b C arctan a b a 0 to rewrite the trigonometric expression in the form asin BO bcos BO cos e O 9 O SVT in 6 DVE cos 6 9 2 9 2 T 9 2 sin 0 9 2 cos 8 O 6 3 cos 6 sin 8 2 2 0 V2 sim 6 VE cos 6 9 2 9 2

X 17 Select the graph of the function below Include two full per TCX

X 8 A television camera is on a reviewing platform a meters from the street on which a parade will be passing from left right see figure Write the distance d from the camera to a particular unit in the parade as a function of the angle x a 25 Not drawn to scale Od 25sec x Od 25cos x O d 25cotx O d 25sin x O d 25tan x am Camera

X 21 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where 0 x 16 x x 4cos 0 16 cos O 4 sin 0 4 cos 0 16 sin 0 4 sin 0

T X 19 Find if possible the complement of 14 O 3T 7 O 13 T 14 O 11 28 O 13 T 28 not possible

6 Period COS 4x Amplitude 11 12 O Period 7 Amplitude O Period 7 Amplitude 7 O Period 27 Amplitude 1 O Period Amplitude 7 2

X 4 Evaluate the following expression x 2 n where n is a whole number sec x sec x tan x sec x sec x tan x 4 4 sec x tan x 3 3 sec x tan x sec x tan x 4 3 sec x tan x 4 sec x tan x

X 20 Evaluate the following expression x n where n is a whole number 5 sec x 5 5 sec x 5 cot x O 5 cot x 5 tan x 5 tan x

X 12 Find the exact solutions of the given equation in the interval 0 2 sin 2x sin x 2 4 0 O X 3 Ox 75 11 X 2 6 6 O x 0 Ox 0 5 7 x 0 O x 0 2 T 3 2 3 5 TL 4 T 3 2 5 TL 3

X 11 Find the period and amplitude y 8 sin x O Period 7 Amplitude 8 O Period 27 Amplitude 1 O 1 Period 7 Amplitude 8 O Period 27 Amplitude 8 Period 27 Amplitude 8

X 10 Find the point x y on the unit circle that corresponds to the real number t O O O t t t t t t 29 6 29 6 29 29 29 6 29 corresponds to the point corresponds to the point corresponds to the point corresponds to the point 1 1 1 11 1 3 corresponds to the point 3 1

1 4 5 12 21 2 5 3 6 8 11

A manufacturer of skis produces two types downhill and cross country Use the following table to determine how many of each kind of ski should be produced to achieve a maximum profit What is the maximum profit What would the maximum profit be if the maximum time available for manufacturing is increased to 60 hours Manufacturing time per ski Finishing time per ski Profit per ski Downhill Cross country 2 hours 1 hour 0 5 hour 60 1 hour 60 Maximum Time Available 48 hours 30 hours How many of each kind of ski should be produced to achieve maximum profit The manufacturer should produce downhill skis and cross country skis Type exact answers Type integers or simplified fractions COXE

problem Round rates to the nearest percent and dollar amounts to the nearest Solve the whole Cent marked down Points 2 The Galerie d Art paid 239 20 for a limited edition Graux point The original Selling Price was 358 80 But this was 53 to make room for incoming piecies what reduced selling Price sale price Does the art gallery lose money if the print sells for the reduced price is the

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night For the United States the sample mean was 391 minutes and for Mexico the sample mean was 426 minutes Suppose that the sample standard deviations were 25 minutes for the U S sample and 42 minutes for the Mexico sample The report concludes that on average adults in the United States get less sleep on work nights than adults in Mexico Is this a reasonable conclusion Support your answer with an appropriate hypothesis test Use 0 05 Use for Mexico and for the United States USE SALT State the appropriate null and alternative hypotheses in minutes Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value MY NOTES State the conclusion in the problem context We fail to reject Ho It is not reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico We fail to reject Ho It is reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico We reject Ho It is not reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico We reject Ho It is reasonable to conclude that on average adults in the United States get less sleep on work nights than adults in Mexico M BA Projec 1 p ompare RP1 Biki Bik Forum Project C Screen 023 0 Screen

Solve the compound inequality and give your answer in interval notatio 3 3x 3 3 12x 9 AND 7x 6 5x 18

Solve the compound inequality and give your answer in interval notation 5x8 22 OR 3x 42 14

Solve the compound inequality and give your answer in interval notatic 9x74x27 OR 2 4x 3 8 10x 6

Express the inequality m 3 1 using interval notation

The following table lists all of your coworkers An X denotes the pairs of people who do not get along Andy Dylan Han Tayshaun Andy X X Dylan Han X X O Dylan and Han O Dylan and Tayshaun X Tayshaun X In making a graph to represent these conflicts which of the following coworkers would have an edge between them O Andy and Dylan Han and Tayshaun

e 1 sin 0 1 cose cose

1 1 1 cosx 1 1 cosx 2csec x

b COS X 1 sinx COS X 1 sin x x15ml 1 2 tan x

1 Solve for x and simplify the answer a 6x 2x 3 0 to no pignus b 2x 4x 5 0 c 2x 2x 3

60 X

Santa s sleigh is flying at a constant height above the ground It drops a present which follows a parabolic path described by the equation h 0 5t 2 5t 10 where h represents the height in meters and t represents the time in seconds How long does it take for the present to hit the ground

1 Tane Tane 1 1 Tane