iyı , Z2 = x2 +iy2 than Z,Z, in polar forr + 62) – i sin(0, + 02) Z,Z2 = ir2(cos(0, – 02) + i sin O Option 2
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Q: (Picture of question is attached)
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A: we have to evaluate the following
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Q: Find the slope of the tangent line to polar curve r = 8 – 7 sin 0 at the point (8 %3D 2' 6
A: Given the equation of polar curver=8−7sinθ .......(1)(8−72,π6)
Q: i HW/ O change from. polar to Cartesian Co-ovdinate's (3, ) vE-2- Cose ... 1,0) © (-4, 3), @ (5,…
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Q: a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A…
A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…
Q: 1.5 3-X Evaluate the integral *dy dx using polar coordinate
A: Follow the procedure given below.
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Q: 1)Basically, what changes when we exchange the Cartesian coordinates for the polar coordinates? 2…
A: Since you have asked multiple question, we will solve the first question for you. If youwant any…
Q: 5. Consider the two curves r= / cos(0) and r= V2 cos(0), -T/2<0ST/2,whose polar plo 0.6 0.4 0.2 0.2…
A: Here, the given curves are: r=cos θ & r=2cos θ
Q: Find the points of horizontal tangency to the polar curve. r = 3 csc 0 + 5 0 < 0 < 2n (r, 0)…
A: Solution:- Given, r=3 csc θ+5 0≤θ≤2π To find Horizontal tendency, find horizontal tangent lines…
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Q: Find the points of horizontal and vertical tangency (if any) to the polar curve. (Order your answers…
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Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int
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A: z1=-3+3i,z2=2+2i,z1z2=-3+3i2+2iApply complex arithmetic rule: a+bic+di = c-dia+bic-dic+di =…
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Q: Let (r, 0) be polar coordinates of the point (x, y) with r2 0. Then we have x = r cos 0, y =r sin 0,…
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Q: Find the points (x,y)at which the polar curve r=1+sin(θ), −π/4 ≤θ≤π/4 has a vertical and horizontal…
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Q: 11 Final the directrix of the polar curve r = 9-2 cos 0 11 99 x = 2 99 2 0 x = - 11 x = -
A: To find- directrix
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A: In this question, we can check one by one parametric equation in the given curve.
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Q: Find the rectangular coordinates of the point(s) of intersection of the polar curves r= 2 sin(2 0)…
A: This question is based on conversion of polar coordinates to rectangular Cartesian coordinates.
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- If the integration by parts was used to integrate the product of e^ax and sin(bx) and cos(bx). e.g.∫e^ax cos(bx)dx and∫e^ax sin(bx)dx. Use Euler’s Identity to evaluate the integral∫e^ax cos(bx) dx+i∫e^ax sin(x) dx =∫e^ax(cos(bx) +isin(bx)) dx =∫e^(a+ib)x dx. Remember that i is a constant! Write the number i in polar complex form and use Euler’s identity to find√i. Hint: The two roots are evenly spaced around the unit circle and√i=i^1/2.2.11 Let A = p cos 9 ap + pz2 sin az (a) Transform A into rectangular coordinates and calculate its magnitude at point (3, -4 , 0). (b) Transform A into spherical system and calculate its magnitude at point (3, —4, 0).If Z1= −4+j8 , Z2= 8−j5 , Z3= 3−j7 and Z4= −8−j9 determine ln(Z2) in both Polar and Rectangular forms.
- The function f (x) = 10 + 2 cos(14x) + cos(11x) + 2 sin(7x) − cos(4x) + 5 cos(3x) is called The Fairy Godmother curve by its shape in polar coordinates. Find the length ||f(x)|| of this curve.Express the functions ƒ(x, y) = (x2 + y2)5/2 and h(x, y) = x2 - y2 in polarcoordinates.Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ as shown in the figure on the right. The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. _ Let R be the region that is inside both C1 and C2. Set up, but do not evaluate, the integral or sum of integrals for the following: (a) the area of R (b) the perimeter of R
- 1) Calculate the complex integrals: For W=0 and W=2, calculate according to the picture where C is the unit circle centered at the origin parametrized as z(t)= eit,t ∈ [-π,π]1) Represent I with the ordered of integration dydx 2) Represent I using polar coordinates1. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x= e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 2. Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = e−2t cos(2t), y = e−2t sin(2t), z = e−2t; (1, 0, 1) 3. Reparametrize the curve with respect to arc length measured from the point where t = 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 4t i + (5 − 2t) j + (1 + 3t) k
- The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. 1) Let P be the point of intersection of C1 and C2 in the second quadrant. Find polar coordinates (r, θ) for the point P where r > 0 and θ ∈ [0, 2π].2) Let R be the region that is inside both C1 and C2. Set up, but do not evaluate, the integral or sum of integrals for the AREA and PERIMETER of R.1) Calculate the complex integrals with Cauchy's integral formula For W=0 and W=2, calculate according to the picture where C is the unit circle centered at the origin parametrized as z(t)= eit,t ∈ [-π,π]3. Transform x^2+y^2-2x+y-2=0 from rectangular to polar