8 Q7: The cartesian coordinates of the polar point (1.n) is (a) (-1.0) (b) (1.0) (c) (0.1) (d) (0.-1) (e) Name

Q: 5. Convert the given functions into the desired coordinates. (a) 2x-5x³=1+xy into polar coordinates,…

A: Solution of this question is :

Q: 4. r2 = 9 sin 20 π TT TT 4 3. 2 r Check for symmetry polar axis line 0 = pole

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Q: 13πt Match the point in polar coordinates 3, 4 04(3, 1) 3π 4 C(3, -t) D(-3, =) OB 3, OD Ś to the…

A: This question can be solved using the concept of polar coordinates.

Q: Q2 Q1 Find the points of intersection of the polar curves r-cos 0 = 0 and 2-cos-r=0

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Q: 4–x2 Sở SY dy dx using polar Evaluate 2x-x2 Coordinates.

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Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: Q2: Sketch the polar function r = 6 cos 30 ,-n <0 < T

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Q: 2. Compute [²√x by first changing it to polar coordinates. 1 -√3x (x² + y²) ² dy dx

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Q: Find the exact length of the polar curve described by: r = 5e 7 on the interval 2 0.000118

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Q: - A tangent at the pole to the polar curve = V2 – 2 cos0 is 0 = r = A 3

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Q: 25) Evaluating in polar coordinates: 6*L*(x² + y²)dydx

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Q: 3 4. Sketch the region described in polar coordinates by r < Cos e

A: We need to sketch the region.

Q: (). 3 Calculate the length of the polar curve r = 8 sin' 3 in the interval 0 < 0<.

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Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

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Q: r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis

A: rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…

Q: Find the exact length of the polar curve described by: r = 8e 3 on the interval a <o< 9n. 2"

A: The length of a polar curve r=fθ in the interval α≤θ≤β is given by L=∫αβfθ2+f'θ2dθ. The given curve…

Q: r2 = 9 sin 20 TT π TT 0. 6. 4 3. Check for symmetry line 0 = pole polar axis

A: r2=9sin2θ When θ=0, r2=9sin20⇒r2=0⇒r=0 When θ=π6, r2=9sin2π6⇒r2=932⇒r=±332 When θ=π4,…

Q: 2. \ Evaluate •V4-2² dydx + dydx 2x-r2 using polar coordinates.

A: We have to evaluate the integral using polar coordinates.

Q: 5(a) Find the slope of the tangent line to the polar curve r = 2sin0 -3cos0+1 at 0= 1/4

A: Using slope formula we have

Q: Q 2. (a). Express z = 3 + V3i in polar form. (b). Find the value of z if e =1.

A: Given : a. z=3+3i

Q: 12. (a) Sketch the curve in the polar coordinate system with directions, (b) Find the values o for…

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Q: Compute the length of the polar curve. r = 1 + θ for 0 ≤ θ ≤ π/2

A: It is given that,  r=1+θ  for    0≤θ≤π2

Q: Draw the polar curve to ((x-3)2/32) - (y2/32) = 1

A: We have to draw the polar curves to x-3232-y232=1.

Q: 3) (a) Find the intersection points of the polar curves r = 3 + 2sin0 and r = 2

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Q: Find an equation (in polar coordinates) of the line tangent to the cycloid x = t - sin t, y = 1 -…

A: Given equations are,

Q: find the slope of the tangent line to the polar curve at the point:

A: From the given expression we find

Q: Test for symmetry and graph polar equation

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Q: Q2: Sketch the polar function r 3 6 cos 30 ,-n<0 < m

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Q: Q1/Prove that the polar expression for the function y = Vx2 - (x2 + y²)3/2 is r = cos20 Q2/Find the…

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Q: 3. Which of the following is the equation of the tangent () line to the polar curver = sec at the…

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Q: Find the length L of the polar curve r = 6 sin for 0 < 0 <- 2 2 OL= 12 OL= 6 OL = 6/2 OL = 12 – 6/2

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Q: 2. Consider the polar curve r = 0² + cos(0) where 0 < 0 < 5. Which of the following values of 0…

A: note : in polar coordinate r=k , where k is a constant , represents a circle of radius k centered at…

Q: 6. Find the length of the polar curve r = 1+ cos 0 on the interval 0 < 0 < n.

A: Given:

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

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: 3) Use polar coordinate to evaluate S'S_√x² + y² dxdy.

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Q: 39 9. A curve with polar equation r = 6sin0+13cose represents a line. This line has a Cartesian…

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Q: 7. Find the exact length of the polar curve: r= 0² , 0<0<2T

A: We will use following formula to find Length of the polar curve  integrationr2+drdθ2dθ

Q: 37. The polar equation of the curve is expressed as r-2sine + 2 cose.. Compute the area bounded by…

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Q: 7. [10pts] Calculate the slope of the tangent line to the polar curve r = when 0 cos (0/3) at the…

A: given curve is                                  r=cosθ3 at   θ=π…

Q: 10. Sketch the polar region inside the graph of r=10 and outside the graph of r=5 from 0 = to 0 = 6.

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Q: 8. 8. Choose the polar curve r=1+ cose. r 1+cos0 (5점)

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Q: b. Plot the polar curve r= 2(1- cos0) in interval t ,2n

A: Given equation is r=2(1-cosθ)  =2-2cosθ

Q: 4. Consider the polar function r(0) = 2+2 cos(20), for 0 E [0, 27). (a) Write parametric equations…

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Q: 8. Find the equation (in terms of Cartesian variables r and y) of the tangent line to the polar…

A: Given curve is Firstly, we find slope of tangent to polar curve is

Q: The Cartesian equation of the polar curve r = 6 sin 0 is (x – 6)² + y? = 36 - (x – 3)² + y² = 9 O a?…

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Q: 2 3 4 Identify the coordinates of the point in polar form based upon the given conditions. Use pi…

A: see below the answer

Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

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