A polar equation is given. 2 - cos(0) (a) Express the polar equation in parametric form. (x(t), y(t)) =

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Given  equation r=2+3sinθwe have…

Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and - the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the identity cos 20 = cos² 0 – sin² 0 to find a polar equation of the hyperbola x² – y² = 1.

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Q: What type of polar curve does the equation r^2 = 4 cos 2@ represent ?

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Q: Find an equation in x and y that has the same graph as the polar equation r- sin 0 = 0 and graph on…

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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: 47. Show that every line that does not pass through the origin has a polar equation of the form sin…

A: Let's understand the relationship between polar coordinates and Cartesian coordinates. Please see…

Q: 45. The rectangular equation x² + y² - 2x=0 written in polar form is r = 2 cos.

A: The rectangular equation is x2+y2-2x=0

Q: dy at the point 1.- dx For the polar equation r=1–cos 0 , find the value of 2 O 1 O -1 O 2

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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: 7. The polar equation of the curve r + y² = 2x is r= 2 cos 0 T= sin 20 T= 2 sin 0 D T= cOs

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Q: Find a polar equation in the form r cos (0 - 0) = ro for the line x = - 12.

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Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

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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: The polar equation 9 cos 0 + 2 sin 0 = X + 1 9x + 2y 1 9y + 2x = 1 9x + 2y = x² + y² || || 1 - r in…

A: To find  the cartesian form of the given polar equation.

Q: Find the slope of the line tangent to the polar curve at the given point. 11n r= 4 sin e; - 2,-

A: Given,            r=4sinθ ; -2,11π6

Q: Find a polar equation for the curve represented by x2 + y2 = 8cx, where c is a constant.

A: The given equation is x2 + y2 = 8cx   Known fact x=rcosθy=rsinθ

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 dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Topic  = Derivatives

Q: 9. Sketch the polar curve. r = 2 cos 2 0

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Q: A particle moves along the polar curve r = -4+ 4 sin 0 in such a way that the angle between the…

A: r = -4+4sinθ  dθ/dt= 5 unit/sec  Find dr/dt when θ = π/2

Q: Find an equation in x and y that has the same graph as the polar equation r-sin 0 =0 and graph on…

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Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: Find the attached handwritten solution.

Q: 9. Sketch the polar curve.r= 2 cos 2 0 ||

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Q: Part A, B, and C

A: According to the given information it is required to sketch the graph of the given polar equation.…

Q: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

A: The polar equation is r=2+3sinθ. Recall that fact that x=rcosθ,y=rsinθ. That is,…

Q: 4. Find the exact length of the polar 2 cos os 0, 0 < 0 < T. curve r

A: Given: r=2cosθ on 0,π L=Length of Polar curve= ∫ab(r(θ))2+(r'(θ))2dθ now, r'(θ)=ddθ(2cosθ)=-2sinθ…

Q: 4 4. a) Identify the conic section given by the polar equation and also determine 1-cos e its…

A: We convert the equation into rectangular form first This is a parabola.

Q: 9. (a) Find the rectangular coordinates of the point(s) of the graph of the polar equation r = 4 sin…

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Q: Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ…

A: We need to sketch the curve with the given polar equation by first sketching the graph of r as a…

Q: •5 25-x2 Evaluate (x² + y? )° dy dx by converting to polar coordinates.

A: To evaluate the integral using polar coordinates

Q: (a) The associated parametric curve is one-half of what familar conic? Sketch the exact curve. r (t)…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question...…

Q: 1. Transform the polar equation 4 cos 0 cos² 0 + 1 into its Cartesian form and identify the curve.

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Q: 6. Consider the polar curve r = 1 – 2 cos(0). Find (a cartesian equation for) the tangent and the…

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Q: 8 sin ( *(4) in the interval 0 < 0< . Calculate the length of the polar curve r =

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

A: Given,  r=9+2 cosθ

Q: The graph of the curve given by the parametric equations x= sint and y=cos2t IS a

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Q: 1 Sketch the curve r=-+sin0 cos 0 ,0 < 0<2n in the polar plane.

A: Any point on the Cartesian coordinate system is represented as x, y. Any point on the polar…

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

A: Given:

Q: Sketch the graph of the polar equation.r = e2θ, θ ≥ 0 (logarithmic spiral)

A: Consider the given polar curve to be r=e2θ, θ≥0.

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: cos (0.48-j0.38) express in polar form

A: we have to express cos 0.48-j0.38 in polar form: we know that cosx-jy=cosxcoshy+jsinxsinhy Now, here…

Q: Example 7 Sketch the curves (c) r 0 (0 > 0) in polar coordinates.

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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: Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an…

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Q: Sketch a graph of the polar equation r2 = 4 cos 2

A: Given:       r2=4 cos2θ First, notice that             r2=4 cos2θ⇒4 cos2θ=2cos2θ Applying following…

Q: The parametric equations: x =ac a cos³ 0,y = a sin 0;0 <0s 2n, define a curve called an asteroid

A: Please refer the attached image for complete solution. THANKYOU.