Trigonometric equations Questions and Answers

Solve the triangle a 4 b 9 c 7 0 A Do not round until the final answer Then round to the nearest degree as needed O B Do not round until the final answer Then round to the nearest degree as needed O C Do not round until the final answer Then round to the nearest degree as needed

Translate to an algebraic expression 5 more than n The translation is

5 J Consider the mathematical system defined in the table Assume that the associative property holds for the given operation Complete parts a to h below VD its and some comma Capitis ww OC No the system is not commutative An example is L 5 5 L O D Yes the system is commutative An example is 5 L 5 L a h Is the mathematical system a commutative group Explain Select all that apply 00 A No The set of elements is not associative under the given operation B No The set of elements is not commutative under the given operation C No There is no identity element for the set under the given operation D Yes It meets all five requirements needed for a mathematical system to be called a commutative group OE No There is at least one one element that does not have an inverse under the given operation F No The set of elements is not closed under the given operation

A 45 X Find x D B K 45 26 26 C X x Give your answer as a simplified radical En

Based on the FCI if 1 500 families attended the sporting event this weekend how much revenue would be generated for the team Bears Ticket X Coke 5 Other Hot Parking drink dog permit 6 3 20 Program 7 Ball cap 10 FCI 138

Find the product of the complex numbers Leave your answer in polar form Z 2 cos 80 i sin 80 Z 6 cos 25 i sin 25 Choose the correct answer below OZ Z2 12 cos 105 i sin 105 OZ Z2 8 cos 2000 i sin 2000 Z Z2 8 cos 55 i sin 55

27 cos x sinx x cos 2x 28 1 cos 2x 2 sin x 2 2 29 sin x cos x 1 sin r

G R K 0 B Q All the graphs above have equations with form y ab Which graph has the greatest value for b Select an answer Which graph has the least value for b Sel red R Select an answer blue B Which graph has the greatest value for a green C

6 A person that is 5 feet tall is standing 80 feet from the base of a tree and the tree casts an 86 foot shadow The person s shadow is 6 feet in length What is the tree s height Hint similar triangles

Use trigonometric identities and algebraic methods as necessary to solve the following trigonometric equation Please identify all possible solutions by including all answers in 0 2 and indicating the remaining answers by using n to represent any integer Round your answer to four decimal places if necessary If there is no solution indicate No Solution 3cos x 3 0 X Answer How to enter your answer opens in new window Enter your answer in radians as an exact answer when possible Multiple answers should be separated by commas Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used Keyp Keyboard Short O No Solution

Convert the equation y 3x to polar form Then solve the resulting equation for 0 0 5 4 010 B JU si

The diagonals of a rhombus measure 9 inches and 6 inches What is the area of the rhombus

Your response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic x Your response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic X Your response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic X our response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic our response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic our response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic x our response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatio x our response is within 10 of the correct value This may be due to roundoff error or you could have a mistake in your calculatic

306 45 X ect value This may be due to roundoff error or you could have a mistake in your calcula 307 85 ect value This may be due to roundoff error or you could have a mistake in your calcula 310 52 X ct value This may be due to roundoff error or you could have a mistake in your calcula 311 06 X ct value This may be due to roundoff error or you could have a mistake in your calcula eck your calculations

Throughout this problem assume cos 3 a What is cos 0 b What is cos 0 360 c What are the two quadrants could lie in d If sin 0 0 find sin 0

Hind all solutions of the equation Enter your answers in trigonometric form Let 0 0 2m X6 64 0 smallest 8 value gest 8 value Zo Z1 22 ZA 25 11 1 2 cos 12 2 cos sin 2 cos 2 cos 2 cos T 12 i sin 12 7x 12 11x 12 5x 4 sin sin sin 7t 12 2 cos sin 12 11x 12 5x 4 19x 12 X X X x

2 26 cos 57 isin 57 z 21 cos 49 i sin 49 Give an exact answer Express any numbers as integers or simplified fractions Use the degree symbol where necessar Part 0 2 Part 1 of 2 a Find z z2 and write the product in polar form with 050 360

The side lengths for AABC below are a b and c The height of AABC is h Fill in the blanks using the lengths a b c and h to derive the Law of Sines Make sure to use the appropriate upper case or lower case letters b b 3 A ank B Part 1 Use trigonometry to fill in the blanks f 8 Part 2 Part 3 sinB and sin C Rewrite the equations from Part 1 h sin B and h sin C Use the equations from Part 2 to write an equation relating sinB and sin C sinB sinc Part 4 Rewrite the equation from Part 3 sin B sin C

1 5 1 Calculate and plot for e for the following points z c d 37mi a 0 b mi 1 Solution a b c d 1 5 le i 1 3 e ni m f m i 1 m 1 2 3 1 5 1f e 1 e i 1 3 e i 3 e x 3 0 4 0 2 m 1 2 3 mi 36 1 0 2 0 2 0 351 0 006i We take the limit for the sequence eti m m 1 2 3 as moo an have

Show that u sin rsinhy and cos x cosh y satisfy the Cauchy Riemann equations Do you recognize the analytic function f u iv Determine its complex form Solution We have du sin r sinh cos 2 sinh y r x du y y sin z sinh y sin xz cosh y y 4 ez y e iz y 2 cos a cosh y r Hence u and satisfy Cauchy Riemann equations and now we calculate v y cos rcosh y f 6 i e 2i ex y eiz y e e iz iy eix y elz y e ix y e iz y 4 i el x y e i x y 2 v es 6 2 i cos z

Verify the following identity tan XX 1 2 csc cot a Which of the following statements establishes the identity O A tan B tan OC tan 2 2 1 cos x 2 sin 1 cos x 1 cos 2 1 csc a cot a 1 csc a cot a 1 CSC a cat g

Verify the following identity 2 2 sin x cos2x 1 To transform the left side into the right side should be changed to and the left side simplif 1 2 sin x sin x cos x

750 feet 40 feet 40 feet 5 The figure shows a 750 foot tower on the side of a hill that forms a 5 angle with the horizontal Find the length of each of the two guy wires that are anchored 40 feet uphill and downhill from the tower s base and extend to the top of the tower Part a What is the length of the uphill guy wire feet Round to the nearest tenth as needed

Solve the equation on the interval 0 2 1 sin 20 1 What are the solutions to sin 20 in the interval 0 2 Select the correct choice and fill in any answer boxe 2 your choice below OA 0 Simplify your answer Type an exact answer using as needed Type your answer in radians Use intege or fractions for any numbers in the expression Use a comma to separate answers as needed B There is no solution

Verify the following identity O A Which of the following statements establishes the identity B tan 2 O C tan 2 tan tan tan a sec 1 2 1 cos 2 sin 1 cos 1 cos x tan a sec 1 tan a sec 1 tan a

Find x and y com A 76 8 A 20 8734 0 345 0 157 85 Add 2 Vector by com C 5656 0 76 8 1780 0 160 A y

Write the point 2 4 in parametric form using radians Parametric form r cos t h r sin t k

2 Angela and her friend Betty bot Angela s house Point A to Bet distance from her house Point side of the river Point C is so

Your answer is incorrect Find sin 2x cos 2x and tan 2x if sinx sin 2x cos2x tan 2x Your answer is incorrect tan 2x 11 3 31 3 4 5 3 X 10 and x terminates in quadrant III 2 16 S

Solve the equation over the interval 0 2 0 2pi sin 3x sin x cos 3x cos x they both equal to 1

1 24 An electric winch lifts a weight on the end of a 3 m jib pole Determine angle for the position shown Figure P1 24 4 m 0 3 m FIGURE P1 24 5 5 m

4 2 Points DETAILS Sketch a graph of the polar equation 7 Need Help 0 Express the equation in rectangular coordinates Use variables x and y O A 2 O 5 5 15 10 5 A 2 0 0

Match the polar equation with the graphs labeled I VI Use the table to help you r sin 30 Select 11 E 111 IV V Select v M Need Help E IV 0 0 V Read It II Watch it VI D 3

x y Need Help 7 1 Points x y Read It Find the rectangular coordinates for the point whose polar coordinates are given 5 57T Need Help DETAILS Read It 18 1 Points DETAILS Watch It Find the rectangular coordinates for the point whose polar coordinates are given 0 18 T

Solve for the unknown parts of each triangle if they exist Show your work 5 B 103 c 10 2 b 7 8

5 6 Points DETAILS TI A corporation creates a sinking fu compounded weekly Round you How much interest would they ear

Verify the identity secx tan x 1 sin x 1 sinx To verify the identity start with the more complicated side and transform it to look like the other side Choose th correct transformations and transform the expression at each step secx tan x Do not simplify Factor out the greatest common factor Apply a Pythagorean identity inside parentheses Apply the appropriate even odd identity inside parentheses

Verify the identity tan x sec x tan x sec x Which of the following four statements establishes the identity A tan x sec tan x sec x B tan x sec X O D X tan x sec 2 tan x sec x 2x sec X tan X tan x sec x tan x sec 2 tan x sec x tan x 2 tan x 11 sec 2 sec X X tan x sec x tan x sec x tan x sec x tan x sec x tan x sec x tan x sec x tan x sec x X tan x sec x tan x sec x tan x sec x tan x sec X tan x sec x tan x sec x

Verify the identity tan 0 cos 0 csc 0 1 Which of the following four statements establishes the identity OA tan 0 cos 0 csc 0 cos sin 0 B tan 0 cos 0 csc 0 cos 0 sin 0 cos 0 sin 0 O c tan 0 cos 0 csc 0 O D tan 0 cos 0 csc 0 sin 0 cos cos cos 0 cos cos 0 1 cos 1 cos 1 sin 0 1 sin 0 1 1 1 1

Verify the identity sec 0 cos 0 tan 0 sin 0 To verify the identity start with the more complicated side and transform it to look like the other side Choose the correct transformations and transform the expression at each step sec 0 cos 0 cos Factor out the greatest common factor Separate the quotient into two terms Apply a reciprocal identity

Let u a a2 and v b1 b be nonzero vectors in the plane and let O be the angle between them The dot product of u and v is defined by u v a b2

Suppose that h t represents the height of a tomato in feet t seconds after it was launched into the air Interpret each of the following mathematical statements in plain English 1 h 3 40 2 h 4 4 h 4 h 2 4 2 4 h 5 32 17 3

5 SET UP ONLY Rewrite the triple integral using cylindrical form Only sketch the xy portion y x y dzdxdy y dzdxdy 8 points 0 1

Determine the amplitude and period of the function Graph the function y cos 6x

Graph two periods of the given tangent function tan x 1 10 y Choose the correct graph of two periods of y tan O A B in x 354 10 below C D 311 15

Determine the amplitude and period of the following function Then graph the function 2 y 5 sin x The amplitudo in

Graph two periods of the given cotangent function y 2 cotx Choose the correct graph of two periods of y 2 cotx below A 3r 57 B f2n Q C 2x Q O D

Calculate the angle of impact for the drop shown Width 1 5 cm b 30 degrees Length 3 0 cm C O 0 008 degrees O 26 5 degrees 60 degrees

Graph the complex number 2 5i

Write the complex number in polar form with argument 0 between 0 and 2 1 i