Given that z = 1- iv3, express z in the form r(cos 0 +i sin 0). Hence write down z' in the form rei®.

Q: Express the number 7√3-3i in the form R(cos(0) + i sin(0)) = Rei, where R> 0 and ≤0 ≤TT. NOTE: Round…

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Q: 2. If z = cos 0 + i sin 0 where 0 is real, show that 1 1 - i tan- = - 1+z 2z 1-z2 Express: а) 1+z2…

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Q: Find the product of zı and z2 Given zı = 4 (cos 180 ° + i sin 180 °) and Z2 = 4 (cos 145° + i sin…

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Q: Given the integral [sec (x - 1) tan4 (x − 1)dx, which of the following equations will be useful for…

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Q: Find sin u and cos u if the terminal side of u lies along the line y =- 2x inquadrant II.

A: Given: Line y=-2x in quadrant II. Note: 1] sinu is positive in quadrant II 2] cosu is negative in…

Q: If x=sin@,y=0 ,y=cosp0,Prove that (1-x²)y,-xy,+p°y=0

A: Given, x=sinθy=cospθ Required to prove, 1-x2y2-xy1+p2y=0...1 Then finding dydx by using chain rule,…

Q: find the four non zero terms in the maclaurin serise for sin h-lx

A: Formula Used: We will need following binomial expansion:

Q: IER, t> 0, u(x,0) sin(87r) cos(90z). u + ru, =x

A: Solve partial differential equation by Lagrange method. Rewriting partial differential equation…

Q: ) Prove that 2+sinZA Cos A-SinA

A: To Prove: cos3A-sin3AcosA-sinA=2+sin2A2

Q: Prove the trigometr 1-Cos (o) Secco) I +seclo) Sina co)

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Q: x+(1/x)=2 cos theta , then show that x2+(1/x2 )=2 cos2 theta

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Q: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

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Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: Show that sin 3x and cos 3x are orthogonal on [−π, π].

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Q: 1 Prove that sec 03D Cos 0

A: Let P(x,y) be a point on a circle of radius r associated with the angle θ.

Q: Find all values of x in the interval (0, 27] that satisfy the equation sec2 x + 2 cos² x = 3

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Q: Evaluate the principal 5th root of z = 50 (cos150° + j sin150°) and find the absolute value (r).

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Q: Eliminate the parameter: I = sin 3t, y = cos 3t, 0 <t <T/3. = COS

A: x= sin 3t     and y=cos 3t     for    0≤t≤π3 We need to eliminate the parameter i.e. we have to…

Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: Find the exact length of r = 3 sin 0 + 4 cos 0. II

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Q: 3. Prove that: tan-1z +z %3D

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Q: 2) Verify that the equation is an Identity. tan 0 = sin 0 %3D sec 0

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Q: Use the Intermediate Value Theorem to prove that sin x − cos x = 3x has a solution, and use Rolle’s…

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Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: If z =7 tan 0, express sin (20) as a function of z. sin (20) =

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Q: Evaluate et sin z cos z dr I COS using Simpson rule with h 20

A: Simpson rule  ∫abf(x)dx=h3f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(x4)+⋯+4f(xn-3)+2f(xn-2)+4f(xn-1)+f(xn) Where…

Q: Given that sin-(x) = a and cos-(x) = B show that sin(a + B) = 1. %3D

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Q: Given the integral sec6 (x − 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: The given integral,       ∫sec6x-1tan4x-1dx

Q: Show that the equation sin(cos 2x)= V1-4x² is an identity. %3D

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Q: Show that given that z = sin-12 дхду дудх

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Q: (1 + cos 9t) 2 sin 9t dt

A: ∫0π1+cos9t2 sin9t dt Consider, ∫1+cos9t2 sin9t dt Put, 1+cos9t=u⇒0-9sin9t=dudt⇒-9sin9t dt=du⇒sin9t…

Q: state what method applies and how one applies it, but do not evaluate the integral:

A: Given integral is We will evaluate the integral by substitution method.

Q: Find a numerical approximation to the length of c(t) = (cos(4t), sin(8 Use decimal notation. Give…

A: Given

Q: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

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Q: We have - (cos (u) du=

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Q: Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard…

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Q: Can the Intermediate Value Theorem be used to prove that the equation 9 2(r + 9) sin*(x) – 4 cos"(x)…

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Q: Find all values of sin-V2 Given Z, = -1 + iv3 and Z, = -v3+i, show that In (Z,.Z2) # lnz, + InZ2 %3D

A: (a) We have to find all values of sin-12

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: Express 6(cos 2pi/3 + i sin 2pi/3) in the form of a +bi

A: Here the given polar form of a complex number is 6(cos2π3+isin2π3) . Now we express the polar form…

Q: -Tt/2 Evaluate using Wallis' Formula: 7 sin5 x cos6 x dx

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Q: 5. Integrate the following and show all of your work: sin“ r cos r dr

A: we have to integrate the following

Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

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Q: (1) Given that z = 1-iV3, express z in the form r(cos e + i sin e) Hence write down z7 the form

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Q: Sketch X,(t) and Xa(t) Where X,() = - Sim3t Sin3t %3D 3. X,(e) = /a Sin 3t %3D

A: To draw the graph of functions X1(t)=-13sin3t and X2(t)=13sin3t, substitute different values of t in…

Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: 1- cos 0 1+ cos 0 sin 0

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Q: Find two angles in the interval [0, 360°) such that sin(x) = -0.61566 %3D

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Q: To evaluate the integral 1 sin20 A sin cose= 2 1-cos20 B sin²0= 2 1 + cos20 (c) cos²0=- 2…

A: In this question, we want to know which identify is useful to solve the Integral.

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.