The equation r = 4 sin 0 + 4 cos 0 represents a circle. The cartesian equation has the form: (x – A)? + (y – B)² = R² %3D where A = B and the radius: R

Q: Given the parametric equation: x=cos(3t), y=sin(3t), 0 less than or equal to t less than or equal to…

A: Given: x=cos3t ,y=sin3t, 0 ≤ t ≤ π2

Q: Find an equivalent equation in rectangular coordinates. r = 10 sin 0 x2 + y2 = 10x %3D VZog2 = 10x…

A:

Q: Given the parametric equations x = 2(8 – sin®) and y= 2(1 - cose). The slope of the tangent line to…

A:

Q: Find a rectangular equation of the portion of the cycloid given by the parametric equations x = a(θ…

A:

Q: Find the circumference of a circle described by the parametric equations = 7 cos 0 and y = 7sin 0…

A: The formula L=∫dxdθ2+dydθ2dθ is formula for length of arc in polar coordinates. As we go along the…

Q: Consider the curve given by the parametric equations = 3 cos 0 and y = 3 sin 6, 0<0<T. Which of the…

A:

Q: Sketch the line and find Cartesian equation for them. r cos(u + 3pi/4) = 1

A: Given, r cosθ+3π4=1

Q: A ball is kicked upward from the ground, with an initial velocity of 44 meters per second, at an…

A:

Q: Show that cos 120 cos 40 – 3 cos 40 sin? 40 and use this identity to find an equation in rectangular…

A: We have to show that cos12θ=cos34θ−3cos4θsin24θ Consider  cos12θ=cos34θ=cos3P        Let P=4θ We…

Q: • Graph the cardioid r a(1 + cose), a <0? • Graph the cardioid r = a(1+ sin6), a < 0? Graph the…

A: Graph are given below:

Q: Sketch the curve and Find the length if the curve: x=cos(2t), y=sin(2t), 0<_t<_ pi/2

A:

Q: Give the center and radius of the circle generated by the equations x = 3 sin t, y = -3 cos t, for 0…

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve, and sketch the curve and indicate…

A:

Q: Find the parametric equation of the line through a = 3 A co which is parallel to b = 2

A:

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: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: Change the equation to rectangular coordinates. r(3 cos e + 4 sin 0) = 12

A: r3cosθ+4sinθ=12

Q: Show that the graph of the equation r=2a cos θ,a&gt;0, is a circle of radius a with center at (0,a)…

A: Given: r=2a cos θa&gt;0

Q: 2:03 AA A mathspace.co E C. 10 11 12 11. Which of following is a radius of the attached circle? JK…

A:

Q: If X =r cose equation (d ,y=r sin@ then show that the will be Erans formed into dy 2. 3D0 dr

A: Change of Variables: Suppose where and Then and

Q: b) r= 3cos(0)-3 sin (0)

A: Idea: substitute x=rCos(theta) and y=rSin(theta) and simplify we get equation in Cartesian form

Q: Consider the parametric equations x =t - sint and y = 1- cost. Which of the following dy ?…

A: If the parametric equations are  given byx=t-sin t  and  y=1-cos tThen to find the value of dydx.

Q: Find dy/dx and d-y/dx, and find the slope and concavity (if possible) at the given value of the…

A: Given: x=6 cosθ, y=6 sinθ a) dydx at the point θ=π4 can be calculated as, dydxθ=π4=dydθdxdθθ=π4…

Q: Write the parametric equations x = 2 sin? 0, y = 9 cos? 0 in the given Cartesian form. y = with 0 <…

A: Simplification of the functions helps to find the parametric equation. Trigonometric identity…

Q: we all know that in "parametric land" x = cos (t) and y = sin(t) represents the Unit Circle. How is…

A:

Q: GRAPH r(u, v) = u cos vi + u sin vj tuk

A: We need to plot the parametric surface: r(u, v)=ucosvi+usinvj+uk.

Q: The unit circle a + y: =1 can be wrriten in parametric form as x = cos(0) and y= sin0. Find and…

A:

Q: Consider the following parametric equation.  x = 14(cosθ + θsinθ) y = 14(sinθ - θcosθ) What is…

A: Given parametric equations are x=14cosθ+θsinθy=14sinθ-θcosθ

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: The equation p = 2 cos 0 sin o in spherical coordinate defines a sphere of center P and radius R,…

A:

Q: x = tan? 0 and y = sec? 0

A:

Q: we all know that in "parametric land" x = cos (t) and y = sin(t) represents the Unit Circle. How is…

A:

Q: x = 4 cos t and y = 4 sin t 0sts 4

A:

Q: Find dy/dx and d?y/dx2, and find the slope and concavity (if possible) at the given value of the…

A:

Q: X = tan?0 3) Eliminate the parameter and write the corresponding rectangular equation: y = sec?0

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: Consider the following. x = sin(0.5θ),    y = cos (0.5θ),    −π ≤ θ ≤ π (a) Eliminate the parameter…

A:

Q: Consider the following. x = sin coso), -n s 0 sa co). (a) Eliminate the parameter to find a…

A: Our objective to find the cartesian equation of the curve.

Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…

A:

Q: Given x= sin 0, y = cos 0, n <o< 2n a) eliminate the parameter to find the rectangular equation of…

A:

Q: Consider the following. x = tan?(0), y = sec(e), -1/2 < e < n/2 (a) Eliminate the parameter to find…

A: x=tan2(θ) and y=sec(θ) knowing that tan2(θ)=(tan(θ))2=sin2θcos2θ and that…

Q: from Equation (3). Then find the length of the indicated portion of the curve. 11. r(t) = (4 cos t)i…

A: The arc length is, 5π/2   The detailed solution is as follows below:

Q: A cyclist is travelling in a straight path at a constant speed along a dirt road with a button stuck…

A: Given: The equations of a cycloid x=rt-sin t, y=r1-cos t.

Q: we all know that in "parametric land" x = cos (t) and y = sin(t) represents the Unit Circle. How is…

A:

Q: Find an upper bound of the absolute value oI e +1 (a) dz, where C is the right half circle |z| = 3,…

A: Note:  Since you have posted multiple questions, which are independent, as per our policy we are…

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…

Q: 2. Given the parametric equation: x= 4 cos (t), y=9 sin (t), 0 <t< 2n, a) sketch the curve and…

A:

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

A: slope is defined at dy/dxand concavity is defined at d2ydx2