Find the Cartesian equation of the image of the line x = 2 under the mappingz → sin(z). Sketch the image. If the pre-image point move on x = 3 from bottom to top, what is the orientation of the image point?

Q: r=1-2 sin(50) -1 V

A: (1) Consider a given polar equation: r=1-2sin5θ we need to find slope and angle of inclination at a…

Q: ) Write the equation r2+r(sin 0-6 cos 0) = 0 in Cartesian coordinates and identify the corresponding…

A: Solution is given below:

Q: The curves T1(t) = (2t, t“, – 4t) and T2(t) = (sin(5t), sin(t), t) intersect at the origin. Find the…

A: Given that  The curves R1 and R2  Intersect at origin  To Find the angle between the curve

Q: Find the equation of the tangent line to the curve y = 2 sin æ at the point (, 1). The equation of…

A: Let (?/6 , 1) =(x1 , y1)  Using the slope - intercept formula : ( y - y1) = m( x - x1 ) or y =mx +b

Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

A:

Q: Find the parametric equations for the tangent line to the curve

A: Here we have to find the parametric equations for the tangent line to the curve,  x=t3-1, y=t2+1,…

Q: Express the curve by an equation in æ and y given (2 sec(t), 5 tan(t)), 0 < t<÷ and identify the…

A: Given x=2sect, y=5tant and  0≤t≤π4

Q: Find the acute angle between the curves xy = -4 and y2 = 2x  If the correct answer is a =…

A: Given xy=-4 and y2=2x

Q: The plot above is created with the parametric equations x(t) = a cos(bt) lylt) = c sin(dt) To…

A: the given equations are as we can see here the domain of x is [-3,3] and the maximum value of x is…

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

A:

Q: Find the equations of the lines that are tangent to at the origin the curve X cos t, Y = 0.5(sin 2t)

A: Please refer the attached image for complete solution.

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: Trace the curve sinecos³e. r =

A: Consider the given equation. r=12sinθcos3θ Check the the symmetry of the curve. he curve is…

Q: Find a cosine equation of the given sinusoidal function. JY

A: we have to find out cosine equation of given sinusoidal function

Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: Using the polar function r = 1 + cos(θ), find the slope of the tangent line at the point (3/2, pi/3)

A: Given: The polar function is, r=1+cosθ

Q: Identify the curve by finding a Cartesian equation for the curve. r2 cos 20 = 1

A:

Q: Please help

A:

Q: 1- Find the equation of the tangent to the 2(x2 + y?)2² = 25(x² . y?) %3D at (3,1)

A: To find the equation of the tangent

Q: In the diagram, AB and BC are both tangent to P. Determine the value of X.

A:

Q: Find the points on the curve y = tan x, -pai/2 &lt;x &lt;pai/2, where the normal line is parallel to…

A: The given curve is y = tanx and normal to the curve is parallel to the line y = –x/2.Differentiate y…

Q: Graph the curve given by the parametric equations below, and show its orientation. x=2 sin t, y=2…

A:

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = sin2(t), y =…

A: Given parametric equation is

Q: Find, correct to two decimal places, the coordinates of thepoint on the curve  y= Sinx that is…

A:

Q: Write an equation for the line tangent to the graph created by the parametric 3 cos 0 and y(0) = 3…

A: To find the equation of tangent line.

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = 2 cos(t), y =…

A: Given parametric equations are

Q: Sketch the following curves and find the points of intersection of the pairs of curves. a) r=…

A:

Q: Find the equation of the line tangent to the graph of y=tanx at the following values of x a) x=0…

A: y =tanxa dydx = sec2xx=0 = 1        (0,0) ∴ Equation of line tangent         (y-0) = 1(x-0)     y=x…

Q: Determine the slope of the tangent line at the pole to the curve r=√2 -2 sinθ Choices: a) 1/2 b)…

A:

Q: TT T 9. x = sin t, y = cos 2t,

A:

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Given equation of curve is

Q: Find the equation of the line that is tangent to the curve y = 6x cos x at the point (T, -67). The…

A:

Q: Find an equation in x and y whose graph contains the points on the curve C. Sketch the graph of C,…

A: The given parametric equation is x=cos 2t,   y=sin t,    -π≤t≤π. This implies that, x=cos…

Q: 3. Sketch the graphs of the following curves. (a) r = 2+ sin 0. (b) r= | cos 30| (c) r = sin 0.

A: We have to sketch the graphs of the given curves.

Q: Find the rectangular coordinate equation for the curve x= cost and y=1-sin2t for 0 greater or equal…

A:

Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: Consider the curve y(x) = sin x. Which one of the following statements is true?

A: sinπ2 = 1

Q: Find parametric equations for the tangent line to the curve of intersection of the following two…

A: We have to find parametric equations for the tangent line to the curve of intersection of the given…

Q: Find the slope and concavity of the curves at the given points. r = sin θ,θ = π/6, π/3

A:

Q: Find the equation of the tangent line to the curve y 6x cos r at the point (T, - 67). The equation…

A: As we know that, The slope of the tangent line to the given curve is equal to the derivative of the…

Q: In three-dimensional space, the graph of the equation z = sin(x) is: O a Line O a cylinrical surface…

A: Given,    Z= sin(x)    Sine curve is the curve of the sine function. It is also known as sinusoid.…

Q: Find, correct to two decimal places, the coordinates of the point on the curve y =sin x that is…

A: Given that y=sinx So coordinate point is x, sinx.

Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…

A:

Q: At the given point, find the slope of the curve and the line that is tangent to the curve, as…

A: Given :2x2y-πcosy=3π(1,π)

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

A:

Q: Sketch the curve r = 3 sin 20. a b Show that its Cartesian equation is (x² + y² )° =36x²y²,«

A:

Q: Find the slope of the curver=-6+6 cos 0 at the points 0= + Sketch the curve along with the tangents…

A: Solution: Consider the given polar curve : r = -6 + 6 cos θ Differentiating with respect to θ drdθ =…

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