State an example of: Parametric equation Polar equation Definite integral

Q: Convert the rectangular equation to a polar equation that expresses r in terms of 0. ²=5y (Type an…

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Q: 4- The equivalent of Cartesian equation (x + = 1) in polar equationis:

A: Given: Cartesian equation:   To determine: equivalent polar equation.

Q: Convert the point (-7 3, 7 V3) from Cartesian coordinates to polar coordinates for 0 <0 < 2m. Give…

A: The given point -73, 73

Q: Find parametric equations for the curve x = 5(y - 1)(y - 2) sin y and then plot the curve using a…

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Q: A curve called the folium of Descartes can be represented by the parametric equations x =3t/(1 + t 3…

A: Given

Q: An ellipsoid S has the parametric equation S(0. Ø) = (cos0 sinø, 2sin0 sinø 4cosø) where 0 and øare…

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Q: Discuss the determined the formula of area in polar coordinate with an example ?

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Q: Explain why the vertical-line test used to identify functions in rectangular coordinates does not…

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Q: Solve and show all solutions. Given the parametric equation of a curve: x(theta)=sin(theta)−1 and…

A: Given the parametric equation of a curve: xθ = sin θ -1   and  yθ = θ+cosθ To Find the tangent line…

Q: Use polar coordinates to evaluate " x tan dya

A: We have to evaluate double integral  Using polar coordinates And using by part integral

Q: Convert the point (3,3 7) from polar coordinates to Cartesian coordinates. Give exact values. y =…

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Q: Find the second derivative of y with respect to x from the parametric equation given. Plot the curve…

A: Given that,  x=3+4sinθ ,    y=3cosθ-4 We need to find the value of d2ydx2

Q: The origin in rectangular coordinates coincides with the............ in polar coordinates; the…

A: we have been given blank statement we have to fill it. Statement : The origin in rectangular…

Q: Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates.…

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Q: Given polar equation is r = 2- sin 0

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Q: 18. r = cos"/3' 19. r = cos 20, 0 = "/a

A: Given:- 18.  r= cos(π/3) ,θ = π  19.   r= cos(2θ) , θ = π/4 To find:- Find the slope of the tangent…

Q: Convert the Cartesian coordinate (2,4) to polar coordinates, 0 < 0 < 2n Enter exact value. 0 =

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Q: Find the points (x, y) at which the polar curve r = 1+ sin(0), has a vertical and horizontal tangent…

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Q: Convert the point with Cartesian coordinates (- 3/3, - 3) to polar coordinates. Enter exact values…

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Q: Do a complete analysis to determine the points of intersection of the polar curves r = 4 sin 0 and…

A: We need to find the points of intersection. So,              4sinθ=1+2sinθ⇒sinθ=12⇒θ=π6+2πn,…

Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given:r=6 cosθInterval: 0≤θ≤π2S=2π∫αβ r sinθ r2+drdθ2  dθ

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

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Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given: The polar equation of the curve   r=eaθ  ,  0≤θ ≤ π2 , Axis of revoultion θ = π2   To…

Q: Convert the Cartesian coordinate (3,-4) to polar coordinates, 0 0 r = Enter exact value.

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Q: tion y = 3 3 x to polar form.

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Q: Convert the Cartesian coordinate (-1,-3) to polar coordinates, 0≤ 0 < 2π r = √10 Enter exact value.…

A: Follow the procedure given below.

Q: Area between two polar functions

A: In order to calculate the area between two polar curves, we’ll Find the points of intersection if…

Q: cosh (0.375-j0.485) express in polar form

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Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Given:r=eaθ,0≤θ≤π2,about θ=π2

Q: Change from rectangular to spherical coordinates.

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Q: Convert the Cartesian coordinate (1,-1) to polar coordinates, 0s0 < 2n r = Enter exact value. %3D…

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Q: Eliminate the parameter for the given parametric equations to write an equation in the form of y=…

A: Given x=ln t and y=et

Q: 3t and y = 1+r 3t Convert the parametric equations to polar form, sketch the graph and find Let x =…

A: Given x=3t1+t3 and y=3t21+t3

Q: V8-x2 Use polar coordinates to evaluate dydx

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: We have,

Q: Convert the Cartesian coordinate (6,1) to polar coordinates, 0 < 0 < 2T r = Enter exact value.

A: Let (x, y) is a Cartesian coordinate. The relation between Cartesian coordinates and polar…

Q: Translate the spherical equation below into both cylindrical and rectangular coordinates.…

A: Let x=r sinφ cosθ, y=r sinφ sinθ, z=r cosφ. Notice that xz=tanφ cosθ and yz=tanφ sinθ. Further,…

Q: Convert from polar to rectangular coordinates. (Round your answers to two decimal places.) (3. - )…

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Q: 4 Consider the point (5, –6) in rectangular coordinates. What is the radius in polar coordinates? (2…

A: Known fact: For a rectangular coordinate point x, y, the radius in corresponding polar coordinate is…

Q: Convert the Cartesian coordinate (-2,-1) to polar coordinates, 0<0< Enter exact value. 0 =

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Q: Convert the Cartesian coordinate (3,-2) to polar coordinates, 0 0 r = Enter exact value. Round 0 to…

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Q: Use a graphing utility to graph the curve represented by the parametric equations. x = 4 cos 8 - cos…

A: Use a graphing utility to graph the curve represented by the parametric Equations

Q: parametric equations representing the given curve.  Line passing through (0, 2) and (3, 1)

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Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

A: Consider the following polar equation: r=2sinθ Differentiate r with respect to θ:…

Q: Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates.…

A: Given : rectangular coordinate ( -4 , 5.66 ) Now we find Polar coordinates

Q: convert the point from polar coordinates into rectangular coordinates (−1, π + arctan(3/4))

A: Answer and explanation is given below..

Q: sinh (0.346 –j0.548) express in polar form

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Q: converts from cartesian coordinates (x, y) to polar coordinates (r, theta).

A: To convert Cartesian coordinate of any point (x, y) to polar coordinate (r, θ) We will use x = r…

Q: Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates.…

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Q: Sketch in polar X=Y

A: In Cartesian coordinate system, x is in the horizontal and the y is in the vertical…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.