Complex numbers Questions and Answers

5 Find the exact values of the three trigonometric functions sine cosine tangent of the real number t B a 1 b 1 3 b 5 13 a b

4 Evaluate the trigonometric function using its period as an aid 11

3 Use the value of the trigonometric function to find the sin t sin t 1

6 Use the value of the trigonometric function to find cost 1

40 ABC CBA EN A B C ABC CBA 693 min ABC 1

37 AB BA EN AB BA 63 A B 9 AB

EX 3 Find the value of each expression A log 32 B log 18

6 Find the slope of each line GIVEN a graph or an equation 5 X Find the slope of each line 5 3y 9x 3 Find the slope of the line through each pair of points 7 18 3 5 7

4 Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle Then solve the triangle Round your answer to tw decimal places a 152 B 17 C 12 Law of Sines A 151 b 65 19 c 91 67 Law of Sines No solution Law of Sines A 151 b 91 67 c 65 19 Law of Cosines A 151 b 91 67 c 65 19

9 Provide an appropriate response What happens if C 90 when the law of cosines is applied in the form C2 A2 B2 2ab cos C

3 Use the law of Cosines to solve the given triangle Round your answer to two decimal places A 130 b 7 c 8 a 13 60 B 25 C 25 a 8 B 23 22 C 26 78 a 7 B 23 22 C 26 78 a 13 60 B 26 78 C 23 22 60 R 22 229 26 790

3 Find values for b such that the triangle has no solutions A 24 a 13

4 Convert the expression

10 Establish the identity algebraically Remember your answer is not a yes or no answer You are to show that one side is equal to the other co csc u cotu csc u cot u

2 Use the sum to product formulas to rewrite the sum or difference as a product sin 90 sin 70 O2 sin 90 cos 70 O2 sin 80 sin 0 O 2 cos 80 sin 0 O2 cos 80 cos 0 2 sin 8A COSA

1 Use the product to sum formulas to rewrite the product as a sum or difference sin COS 3 6

Find zw and 2 10 10 W 3 1 Leave your answers in polar form What is the product co Simplify your answers Type exact answers using radicals as needed Use indogers or tractions for any numbers in the expression Type any angle measures in degrees Use angle greater than or equal to 0 and less than 360 What is the quotient con Simplify your answers Type exact answers using radicals as needed Use integers or fractions for any numbers in the expression Type any angle measures in degrees Use angle s greater than or equal to 0 and less than 360

4 Graph the image of parallelogram CDEF after a dilation with a scale factor of at the origin fa 10 6 4 2 centered

Use the Law of Cosines to determine the length of side x 37 15 A 17 X C 24 30 30 B

Solve the following logarithmic function log x 4 2172 O 5224 0603

D If six less than three times x is equal to 8 more than 4 what is the value of x squared

9 The cost c of renting a lane at a bowling alley can be modeled by the equation c 8 5h where h is the number of hours that the alley is rented for If Janet wants to rent 4 lanes for 3 hours each for her birthday party how much will it cost

5 5 13 k 5 10 4k 56

3 5m 1 6 a 1 8 8a a 5 4 4 3r 3r 12 4x 9 3x 8 7x 2x 10

sec sec T R 6 Simplify your answer including any radicals Use integers or fractions for any numbers in the expressi

4 Use the formula asin Bo bcos B0 expression in the following form y a b cos Be C a b cos Be C where C arctan a b a 3 b 7 B 2 to rewrite the trigonometri

Let a h 20 10 and a2 H For what value s of h will the set a a span R X

9 Verify that each equation is an identity algebraically Remember your answer is not a yes or no answer Verify means Prove and this whole proof needs to be part of your answer csc s sin s cos s cot s

5 Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of 0 where cos 0 3 3 81 9x x 3 cos 0 1 0 1 Then find sin an 2

Use the trigonometric substitution x 2 tan to rewrite the algebraic expression 4 x as a trigonometric function of 0 where Explain all of your steps and how you solved it 2 x

8 If x 5 sin 0 use trigonometric substitution to write 25 x as a trigonometric function of 0 where 1 0 1 2 5 cos 0 5 sec 0 5 csc 0 5 tan 0 5 sin 0

Radioactive uranium 235 has a half life of about 700 million years Suppose you find a rock 1 16 and chemical analysis tells you that only of the rock s original uranium 235 remains How old is the rock Select the correct answer below OA 350 million years old OB 1 4 billion years old OC 3 5 billion years old OD 175 million years old OE 2 1 billion years old OF 2 8 billion years old

is the dependent variable decide which variable is the independent variable and whic Choose the correct answer below OA Mathematical models are based on relationships between quantities that can change These relationships are described by mathematical tools called functions The quantities related by a function are called variables because they change A function describes how a dependent variable changes with respect to an independent variable The values of dependent variables depends on the values of independent variables OB Mathematical models are based on relationships between quantities that cannot change These relationships are described by mathematical tools called functions A function describes how a dependent variable changes with respect to an independent variable The values of independent variables depends on the values of dependent variables OC Mathematical models are based on relationships between quantities that can change These relationships are described by mathematical tools called functions The quantities related by a function are called variables because they change A function describes how a dependent variable changes with respect to an independent variable The values of independent variables depends on the values of dependent variables O D Mathematical models are based on relationships between quantities that cannot change These relationships are described by mathematical tools called functions A function describes how a dependent variable changes with respect to an independent variable The values of dependent variables depends on the values of independent variables

Use the theoretical method to determine the probability of the following outcome and event State any assumptions made Tossing two coins and getting either one head or two heads Choose the correct answer below O A O B O C Assuming that each coin is fair and is equally likely to land heads or tails the 4 O D probability is Assuming that each coin is fair and is equally likely to land heads or tails the 1 probability is 3 probability is 2 Assuming that each coin is fair and is equally likely to land heads or tails the 3 4 Assuming that each coin is fair and is equally likely to land heads or tails the probability is 2 x 2

probability of winning some prize on a single ficket is 1 in 100 What is your probability of having at least one winner among your 25 tickets Choose the correct answer below OA The probability is 0 2510 according to the at least once rule for independent events OB The probability is 1 0 99 25 according to the at least once rule for independent events OC The probability is 0 2510 because each ticket counts as an independent event OD The probability is 1 0 99 25 because the probability of not winning is 1 0 25 25 OE The probability is 25 in 100 because you bought 25 tickets OF The probability is 25 in 100 because the events are non overlapping

Pinocc D write your answer as an integer or as a decimal rounded to the nearest tenth mcc

Click here to watch the video Find the quotient 2 cis 41x 36 2 cis 18 cis 41x 36 11x 36 in rectangular form using exact values 11x 18 cis 36 Simplify your answer including any radicals Use integers or fractions for any numbers in the

Multiply 78 I 5 6 7 5 8 6 Simplify your answer Type an integer or a fraction

7 From the top of a cliff 108 m high the angles of depression of two small boats on the water are 90 and 15 20 Boat A 9 15 2 Boat B Calculate the distance a from the foot of the cliff to the closer boat 108m b between the boats if they are sighted in the same direction

7 Find an angle that has the same cos ratio as 497

6 Find the exact value of tan e when sec calculator 227 e is in Q4 Do not use

Determine two different Hamilton circuits in the following graph Select all that apply A A B C F I H G D A B G E D A B C F I H G C A B C F I H E G D A D G E H I F C B A D G De H

9 In the expansion of 4x 1 the coefficient of the term in x is 1248 Find the value of n

23 Find the component form of v if v 8 and the angle it makes with the x axis is O 8 3 8 O 4 4 3 O 8 8 3 O 4 2 4 2

Use the accompanying sinking fund formula to determine the payment needed to reach the accumulated amount Semiannual payments with 6 interest are compounded semiannually for 5 years to accumulate 40 000 The semiannual invested payment is Do not round until the final answer Then round up to the nearest cent p H 7 nt

8 Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector Initial Point 0 8 Terminal Point 9 12

15 Find values for b such that the triangle has no solutions 1 51 a 10

10 Find values for b such that the triangle has no solutions A 24 a 13

9 Find the component form of v if v 8 and the angle it makes with the x axis is 30 O 8 3 8 O 4 4 3 O 4 3 4 O 4 2 4 2

Does 3 converge absolutely converge converge absolutely n5 AFT converge conditionally or diverge n 1 0 1 505 22