Given points (r1, θ1) and (r2, θ2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as much as possible using the identity cos2 θ + sin2 θ = 1. Hint: Write the expressions for the two points in Cartesian coordinates and substitute into the usual distance formula. (Use any variable or symbol stated above as necessary.)

Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for T. r…

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

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Q: For the polar function r (0) = 3 cos(20) do the following:

A: Given : Polar equation r(θ) = 3 cos(2θ)    To find : Plot the graph of given polar function. And…

Q: The area of one loop of the graph of the polar equation r =2 sin 30 is Select one: O27 3

A: r=2sin3θ

Q: Find the polar coordinates, -pi … theta .... 2pi and r </ 0, of the following points given in…

A: We have r=x2+y2=12+0=1 As we need r≤0, we take r=-1. We know that the angle between the ray through…

Q: Evaluate the polar coordinate E( 4r² cos 0 rdrd@.

A: I have stated the used formulas in the solution

Q: If (r, 0) is another representation for the polar point (3.1, and the angular coordinate is 0 =…

A: Use the concept of polar coordinates and solve the above.

Q: Convert the given polar equation to a Cartesian equation. (Use the following as necessary: x and y.)…

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Q: Find a polar form of the equation. 5x – 3y = 9 sin(50)cos(-30) = 3 OS

A: Given equation5x -3y =9         ----(1)To convert the given equation to polar formsubstitute,x = r…

Q: The polar form of the Cartesian equation x = 4 is Select one: a. r sin 0 = 4 b. r= 4 cosec 0 c. r= 4…

A: We have to find the polar form of the Cartesian equation  x = 4

Q: Convert from polar to rectangular form. Give exact answers when possible. Otherwise, round to the…

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Q: Express the given equation in polar coordinates. 144xy = 121 121 p² sin? 0 = 144 121 ? cos 0 sin 0 =…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. 9 3 cos 0+2…

A: Let's convert to Cartesian equation.

Q: Find the polar coordinates, 0 … theta .... 2pi and r >/ 0, of the following points given in…

A: The given Cartesian coordinates is (1, 1).

Q: 4) Use the conversion formulas æ = r cos 0, y = r sin 0 or r2 = x² + y², tan 0 = to convert the…

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Q: The polar form of the Cartesian equation x = 4 is ... ...... Select one: a. r sin 0 = 4 %3D b. r=4…

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Q: The polar form of the Cartesian equation x = 4 is Select one: a. r sin 0 = 4 b. r=4 cosec 0 c. r=4…

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Q: Without using a calculator, for the following, sketch the graph of the polar equation and identify…

A: Follow the procedure given below.

Q: Which of the following Polar equation represents the following Curve -2 (a)r = 1- sind (b) r= 2+…

A: We have to check

Q: Find the slope of the tangent line to a given polar curb at the point specified by the value of…

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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: Perform the indicated operation and convert your final answer to polar form z = r(cos® + isin®)…

A: Given query is to convert the expression in Polar form.

Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for T. r…

A: We will evaluate the required value.

Q: Which of the following is the polar equation for the graph shown above? Or=1+2 cos(0) Or= 3 cos(30)…

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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: Perform the indicated operation and convert your final answer to polar form z =r(cos0 + isin®) 3.)…

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. 4. 7 cos 0+2…

A: To convert the given equation into cartesian form.

Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for `pi.…

A: to identify the coordinates of the point in polar form

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

A: To determine : The coordinates of the point given in the picture in polar form based on the given…

Q: consider the polar equation defined by r = 5 cos(2 sin 8), where s0< 2n. Determine the missing…

A: as points are already find π6,2.70    π3,-0.80    π2,-2.08  3π4,0.77                      π,5…

Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for T. O…

A: Coordinates of the point in polar form based on the condition will be

Q: Use De Moivre's Theorem to solve for z and leave your answer in polar form with the angle in radians…

A: If z=rcosθ+isinθ then the nth root is zn=rncosθ+2πkn+isinθ+2πkn and if z=a+ib then r=a2+b2 and…

Q: Convert the given polar equation to a Cartesian equation. (Use the following as necessary: x and y.)…

A: We have to convert the polar equation to cartesian equation,  r = 6 sinθ

Q: Which of the following shows the correct sketch of the polar curve r= + 5 cos 0? 4 -6 -4 6 -4 6. b)…

A: r = -(5/2) + 5cos(theta) curve

Q: Which of the following shows the correct sketch of the polar curve r = 6 sin(3 0)? 10 а) -10 10 -10…

A: To plot the polar curve r=6sin3theta

Q: Convert the following polar equation into a rectangular equation. If possible, write the rectangular…

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Q: Use the unit circle to find all values of u between 0 and 2p for which cos theta = - 1/2

A: Given:          cos u = -12 To find:               The values of u between 0 and 2π.

Q: Which of the following shows the correct sketch of the polar curve r = -8 + 8 sin(0)?

A: The given polar equation is: r=-8+8sin(θ)

Q: Find zw and W Leave your answers in polar form. - TC TO Z= 6 cos + i sin 11 11 TO W = 6| cos COS + i…

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Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for T.…

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Q: Convert the following function given in Cartesian Coordinates into Polar form. 25-y 25 Or = cos? 0-…

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Q: are polar coor point P, as shown below, find the maximum possible errors in calculating x and y…

A: In this, We find the maximum possible errors in calculating x and y coordinates of the same point.

Q: Identify the coordinates of the point in polar form based upon the given conditions. Use pi for T. r…

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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: Q2. Discuss the symmetry and plot the polar equation r 2-3 sin 0.

A: Given- r=2-3sinθ To find- The symmetry and plot the above polar equation.

Q: Graph the following polar equation and set up the equation to find the area enclosed by the polar…

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Q: onvert the given Cartesian equation to a polar equation. (Use the following as necessary: r and 0.)…

A: Explanation and solutions is given below.....

Q: Use a calculator to complete the table of coordinates. Where necessary, round to two decimal places.…

A: Complete the table: Evaluate r for given value of θ: θ r=4sin2θ 0 r=4sin0=0 π6…

Q: For the polar equation r = 4+ 2 sin 0 :

A: We have r=4+2sinθ A graph is symmetric about x-axis if rθ=r-θ A graph is symmetric about y-axis if…