Q2. a. Replace the given polar equation by equivalent Cartesian equation = 1. r2 + 2r2 cos 0 sin 0 = r = 4 tan Osec0. i. ii. b. Replace the given Cartesian equation by equivalent polar equation (x + 2)² + (y – 5)² = 16.

Q: . Which of the following is the equation of the tangent at the point 0 = 3 line to the polar curver…

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Q: What is the slope of the line tangent to the polar curve r = ㅠ Ө - ? O 1 √√3 ✓ 2 T -||♡33 √√3 cos at…

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Q: (b) Use appropriate software to sketch the following polar curves i) r = cos(7.10) + cos² (0) ii) =…

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

Q: Please help with this question

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Q: Replace the Cartesian equation with an equivalent polar equation. x² + y² - 4x=0 O A. r cos²0=4 sin…

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Q: Sketch the curve with the given polar equation. r = 1+2 cos 0 7/2 Зп /4 T/4 2 4 57/4 77/4

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Q: The equivalent Cartesian equation of the polar equation r = tan0sec0 is: A) y = x. B) y= x2. C) ху —…

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Q: Which of the following shows the correct sketch of the polar curve r = -9+ 9 sin(0)? 15 5 -15 -10 -5…

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Q: Find the slope of the polar curve r= e® at 0 = n/3.

A: Given:

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: Find a polar equation for the curve represented by Cartesian equation x? = 22y. O A.r = 44 tan 6Osec…

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Q: Find the exact length of the polar curve. r=4 sin(θ), 0<θ< π/2

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Q: The equation of the polar curve above is E. r = 3 + 2 sin 0 F. r = 3 - 2 sin 0 G. r = 3+ 2 cos 0 H.…

A: From the direction of the cardioid, extending horizontally, that you…

Q: Without using a calculator, for the following, determine whether the graph of the polar equation is…

A: Given that    r = 2 secθ            we know that    x(θ) =  r cosθ      and      y(θ) = r sinθ…

Q: 37. The Cartesian equation of the polar curve 2 = 2a' sin 20 is A. 1? + y? = 4a²xy B. (z* + 3° )° =…

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Q: Test the following polar equation for symmetry with respect to the polar axis, the pole, and the…

A: we have been given the polar equation  r=4+8cosθ we have to show the symmetry with respect to the…

Q: Find the length of the curve over the given interval. Polar Equation Interval r = 9 cos(8) 2

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Q: 13n Match the point in polar coordinates 2, to the points A, B, C, or D. 4

A: Here simple we satisfy angle property

Q: Consider the polar equation defined by r= 5 cos(2 sin 6), where 0<0< 2x. Determine the missing…

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Q: Which of the following gives the Cartesian form of the polar equation r = 7 2cos 0+5sin 0 Select the…

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Q: Find dy/dr and the slopes of the tang ent lines shown on the graph of the polar equation r = 2+3 sin…

A: According to question, r = 2 + 3 sin θ

Q: Q2) Replace the following polar equations by equivalent cartesion equations and identify their…

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Q: Q2\ Replace the following polar equation by equivalent Cartesian equation and identify their graphs…

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Q: Find the length of the curve over the given interval. Polar Equation Interval r= 2a cos e 4 4

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Q: Which of the following is the equation of the tangent line to the polar curve r = sec at the point 6…

A: Given,r=sec θ2At θ=π3,r = 23

Q: 7. The equivalent Cartesian equation of the polar equation r=cot ese e is a) y=x c) y=x b) xy 1 d)…

A: Using Cartesian coordinate.

Q: Find the equation of the line tangent to the polar curve at the point. r= 2cos(θ/ 3),  θ =π/4

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Q: 1) (a) Convert BOTH of the below equations from either polar to rectangular or rectangular to polar.…

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Q: Q1// Converting r= 12 cos 0 from polar to the equation of a circle?

A: Solution is given below:

Q: Q1// Converting r= 12 cos 0 r = 12 cos 0 from polar to the equation of a circle?

A: Given problem:- Converting r = 12cos(θ) from polar to the equation of a circle?

Q: 1. Sketch the graph of r = 2 sin(20) in polar coordinate system T/4 31/4 5T/4 7T/4 in the polar…

A: Consider the provided polar equation, Sketch the graph of the polar equation. Now make the graph of…

Q: For the given rectangular equation, give its equivalent polar equation. 6x - y = 14 r= H 14 6 sin…

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Q: 4. Find a polar equation for the curve represented by the Cartesian equation y = 3x. T = r cos 0, y…

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Q: Which of the following shows the correct sketch of the polar curve r= -2 cos(3 0) for 0 <0 < ? 10 -…

A: Use Desmos graphing calculator. Option (b) is correct.

Q: For the given rectangular equation, give its equivalent polar equation. 6x - y = 14 14 r = 6 sin e -…

A: The rectangular equation is given by 6x-y = 14 To evaluate : The equivalent polar equation.

Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

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Q: Test the following polar equation for symmetry with respect to the polar axis, the pole, and the…

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Q: aluate the dnd to polar

A: Given that, ∫0a∫02a-x2xx2+y2dxdy Take x=rcosθ, y=rsinθ where 0≤θ≤2π.

Q: x = 4 cos t and y = 4 sin t 0sts 4

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Q: b, The polar equation for the curve whose rectangular(cartesian)equation xy32 is: (a)rcosesine = 4 4…

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Q: A particle moves along the polar curve r =1– 2 cos 0 so that = 2. Find the value of d at e = , and…

A: We are given that,                     Now,              When          , Then

Q: What is the polar equation of the vertical line x = 13? Choose the correct answer below. A. r= 13…

A: Given data is : x=13 What is the polar equation of the vertical line x=13

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: A Find a polar equation for 1. (x - 3)2 + (y + 1)2 = 4. 2.x2 + xy + y? = 1

A: Find a polar equation for  ( x -3)2 + (y+1)2 = 4 and x2 + xy + y2 = 1. Here i provide full solution…

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: Which of the following shows the correct sketch of the polar curve r = 9 – 9 cos(0)?

A: We have to do following steps to solve it.

Q: Find the length of the polar curve r = 5°; 0 <e< 2n

A: Given ,r=5θdifferentiate w.r.t.θdrdθ=5θ.ln(5)Weknow that length of the curve…