47. Show that every line that does not pass through the origin has a polar equation of the form sin 0 – a cos 0 where b # 0.

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

A: Given problem is :

Q: Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

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Q: 2. Compute dy dx (x² + y²)' by first changing it to polar coordinates.

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Q: Find the slope of the tangent line to the polar curve r = cos(30) at 0 = 7. Enter as an integer or…

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

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Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: Which of the following is an equation of the tangent line to the polar curve r = 2(1+cos 0) at the…

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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: dy = cos 20. de dx Given that r= cos 0 ; = - sin 20 and de The slope of the tangent line to the…

A: Given that: r=cosθdxdθ=-sin2θdydθ=cos2θ

Q: 2. Use calculus to show that these polar curves intersect at right angles. = sin 0, r = cos 0

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Q: Find the slope of the tangent line to polar curve r = 6 – 9 sin 0 at the point (6-

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Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

A: To find the residue of sinz2sinz2 at z=0 and z=π Let  fz=sinz2sinz2=sinz2csc2z…

Q: 1. Change ſ, Lz xy dydx to polar form. 4-x2

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: Replace the Cartesian equation x² + y² equation. OA) r sin² 0 = 4 cos 0 B) r = 4 sin 0 Oc) r = 4 cos…

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Q: Show that cos(18θ)=cos^3(6θ)−3cos(6θ)sin^2(6θ) and use this identity to find an equation in…

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Q: Find the points on the the polar curve r = 4 cos 0 where the tangent line is horizontal.

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Q: Consider the curves:r = 4sin 0 and r = 2 sin(0) + 2cos (0).

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Q: Consider the following parametric equation. #20(cos 0+0 sin 0) y- 20(sin 0-0 cos 0) What is the…

A: Given: x=20cosθ+θsinθy=20sinθ-θcosθ we know length of curveL on interval a,b is given by…

Q: Show that cos21θ=cos^3(7θ)−3cos7θsin^2(7θ )and use this identity to find an equation in rectangular…

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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: = Replace the polar equation 8r cos 0 + 9r sin 0 Cartesian equation. OA) 8x +9y = 1 B) 8y + 9x = 1…

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Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: Consider the following parametric equation. = 5(cos 0 + 0 sin 0) y = 5(sin 0 – 0 cos 0)

A: Given,          The parametric equation are x=5cosθ+θsinθ and y=5sinθ-θcosθ.

Q: 9. Find the length of the curve: r = 1+ cos(20),0 < 0 s 2n

A: given equation of curve r=1+cos(2θ)   , 0≤θ≤2π as per our guideline, we are supposed to answer the…

Q: Find the slope of the tangent line to the polar curve r = 1 + cos(0) at the point specified by 0 =…

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Q: Find the equation of the tangent line(s) to the following set of parametric equations at the given…

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Q: 2. Express in true polar form, z 5(cos 55°-j sin 55°)

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Q: Use an appropriate local linear approximation to estimate the value of cos(29°). cos(29°) -

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

A: To evaluate the integral using polar coordinates

Q: 44. A tangent at the pole to the polar curve r = 2- 4 sin 0 is af pole 0 = = D 0 = Sing 8sin

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Q: Graph the Plane Curve defined by: I = 3 cos(t) - t + 5. y = sin(t). for t in [0, 37]. x Clear + Undo…

A: Plot the points for different values of t from [0,3π]. Draw the curve passing through the points.

Q: dy dx Given that r= cos 0 ; do - sin 20 and cos 20. de = - The slope of the tangent line to the…

A: Explanation of the answer is as follows

Q: dx Given that r cos 0; dy - sin 20 and do = cos 20. de The slope of the tangent line to the polar…

A: Here I am attaching image so that you understand each and every step.

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: dx dy = Cos 20. do Given that r= cos 0 ; = - sin 20 and d0 The slope of the tangent line to the…

A: Slopes of tangent is dy/dx . Finding dy/dx at theta = 0.

Q: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

Q: aluate the dnd to polar

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

Q: 7. Suppose that x2 + y? = r² and x = r cos 0, as in polar coordi- nates. Find дr ax дr and дх

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Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

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

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. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

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: Find the length of the curve: r = /1+ cos(20),0ses 2n

A: The length of the curve is given by the formula ∫abr2+drdθ2dθ  ,       where a≤θ≤b

Q: Find the slope of the tangent line to polar curve r = 3 cos 0 at the point 4

A: Given polar curve is - r=3cosθ We need to determine slope of tangent line at the point 32,π4.

Q: The position of a particle in the xy-plane at time t is given by r(t) = (cos 2t) i+ (2 sin 2t) j…

A: Given: rt=cos2ti+2sin2tj For finding equation in x and y whose graph is the path of the particle, we…

Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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