Scientists and engineers often use polar equations to model the motion of satellites in earth orbit. Let's consider a satellite whose orbit is modeled by the equation r= 22000/(4 - cos(0)), where r is the miles between the satellite and the center of the earth, and e is the angle shown in the following figure.

Q: Find two different parametric equations for the rectangular equation given. y=x* +3 (a) Substitute…

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Q: Sketch the line and find Cartesian equations for it.   r cos (u - pi/4) = (2)^1/2

A: Given, rcosθ-π4=2

Q: Convert the rectangular equation to a polar equation that expresses r in terms of 0. X= 11 r= (Type…

A: Given  X = 11

Q: 5. Convert the polar equation to a rectangular equation. r = -2 sin 0

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Q: Find an equation in rectangular coordinates for the curve r^2 = cos 2θ.

A: We know that, the relationship between polar and rectangular co-ordinates are given as r2=x2+y2…

Q: Sketch the curve represented by the parametric equations x = 2 + sec θ, y = 3 + tan θ (indicate the…

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Q: An equation of the line y=4x-2 in polar coordinates is: r=0 r=-4/(2cose -sine ) O r=4/(2cose -sin® )…

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Q: Convert the Cartesian equation x² + y² + 3x = 0 to a polar equation. r² = = -3 cos 0 r= 3 cose r= -3…

A: Given x2+y2+3x=0To find polar equation:

Q: Sketch the curve with polar equation r = 2 cos0

A: We first make a table of values θ 0 π/4 π/2 3π/4 π r 2 1.41 0 -1.41 -2

Q: a) A curve has the parametric equation given as x = 4+3 cos 0 y = 3 sin 0 – 2. i) Convert the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the polar equations of ALL the tangent lines to r = sin (30) at the origin.

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Q: Sketch the curve represented by the parametric equations x = 8 cos θ,            y = 8 sin θ…

A: given: the parametric equations of the curve are: x=8cosθy=8sinθ

Q: Sketch the curve represented by the parametric equations x = 6 cos θ, y = 6 sin θ (indicate the…

A: The curve represented by the parametric equations x = 6 cos θ, y = 6 sin θ. We need to Sketch the…

Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: Find the exact length of the polar curve. r = 3 sin(0), 0≤0 ≤ π/4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Sketch the curve represented by the parametric equations x = 3 cos θ,             y = 7 sin θ…

A: Given:  x=3cosθ                                                     ...1y=7sinθ…

Q: Find a polar equation for the curve represented by the Cartesian equation: x² = 8y. Or= 8 sin cos 0…

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Q: Convert the rectangular equation to a polar equation that expresses r in terms of 0. x² + (y + 2)? =…

A: Given,  The rectangular equation  x2+y+22 = 4  We have to  convert it in polar equation in terms of…

Q: he Cartesian equation (x – 10)2 + y² = 0 in polar form. %3D

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Q: Find a Cartesian equation for the curve represented by polar equation . r = 14 cos 0- 12 sin 0.

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Q: 4 Convert the equation from polar to cartesian. r = 3 – 2 sin 0

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Q: 2. Transform the polar equation into a Cartesian equation. 4 r = 4 + sin 0

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Q: 4. A horse on a merry go round is 7 m from the center and travels at 1Okm/hr. What is its angular…

A: Let's find.

Q: A pair of parametric equations is given. x = 5 cos(t),    y = 6 sin(t), Find a…

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Q: How do you solve this using polar coordinates?

A: We will find out the required result.

Q: Eliminate the parameter t from the parametric equations x = 3 + sin t and y = cos t − 2. Graph the…

A: Circle equation

Q: Convert (x + 2)² + y² = 4 to polar form. Drag and drop an answer to each box to correctly complete…

A: Let's find.

Q: If an equation fails the test for symmetry with respect to the polar axis, what can you conclude?

A: The equation has failed the symmetry test, but that does not mean that it is not symmetric with…

Q: Write the equations that are used to express a point withCartesian coordinates (x, y) in polar…

A: To convert Cartesian coordinates x,y in polar coordinates. In polar coordinates point is given r,θ.…

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: Find the slope of the polar curve at the indicated point. r = -9 + 3 sin θ, θ = 0

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Q: Find the exact length of the polar curve. 3 sin(0), 0 < 0< 1/2

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Q: Convert the rectangular equation to a polar equation that expresses r in terms of 0. X= 11 (Type an…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. x2 + y2 = 10cx

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Q: Eliminate the parameter from the parametric equations: æ = 3 sin t y = 2+ cos t The resulting…

A: Given: x=3sint                                                                   ..1y=2+cost…

Q: Of a circle of radius "a" whose center is point (1,-1).Write the equation in Polar Coordinates.…

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Q: Convert the rectangular equation x² + y² – 2x = 0 to polar form. Have your equation begin with “r ="…

A: Explained below

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve). x…

A: cos2x+ sin2x=1

Q: Convert the Cartesian equation y = x2 + 2x into a polar equation (you should be able to simplify…

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Q: Sketch the curve with the given polar equation, and find its Cartesian equation. 2 =-4 sin 20 %3D y

A: We are given the polar equation . Let us plot the figure.

Q: The parametric equations: x = a a cos 8,y = a sin 0;0 <e< 2n, define a curve called an asteroid

A: Given: The parametric equation is where 0≤θ≤2π   To determine: The slope of the tangent wrt θ i.e…

Q: 2. Convert Polar Equation to Rectangular Equation. 1 r = sin 0 – cos 0

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Q: A curve in polar coordinates is given by: r= 8+2 cos 0. %3D

A: Given r=8+2cosθ and  P is a point at (r, θ) with θ=18π16=9π8 (a)  to find the  r coordinate of point…

Q: Find the Cartesian form of the equation in spherical coordinates given by p = 2 cos p.

A: We have to solve above question and find cartesian form

Q: 10. Sketch the curve of the polar equation r = 2 sin 0 . Find a rectangular equation for this curve.

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Q: Find the polar equation for the curve represented by the equation y = 1+ 3x. A 1 ,0) sin 0-3 cos 0 В…

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Q: Sketch the graph and the curve represented by x = 3 cos 0 and y = 4 sin 0 ,0 < 0 < 2n by eliminating…

A: The given parametric equation,      x=3cos θ and y=4sin θ, 0≤θ≤2π

Q: (b) Find the graph of the parametric equations: I = sin 0, y = 3 – 2 cos 20

A: Plugging values of θ, to find the corresponding values of x and y: When…