Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

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: Find an equation for the line tangent to the graph of y=tan-1(x) at the point (1,π/4).

A: Given information:

Q: Find the equation of the line that is tangent to the curve y = 4x cos x at the point (T, -47). The…

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Q: Find the equation of the tangent line to the curve y 42 cos z at the point (, The equation of this…

A:

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: 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 an equation of the line tangent to the curve tan¹(y) = (x+y)e at the point (0,0). tan ¹(xy) =…

A:

Q: Find an equation of the tangent to the curve given by tan(0), y = sec(0) at the point (x, y) = (1,…

A:

Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter…

A: Here we have to find an equation of the tangent to the curve at the given point by both parameter…

Q: The curve y = x /( 1+ x2 ) is called a serpentine. Findan equation of the tangent line to this…

A:

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 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: Find the exact length of the curve. y = Vx - x2 + sin

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

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

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: 1. Find a cartesian equation for the curve r² sin 20 = 8.

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Q: Plot the astroid x = cos3 θ, y = sin3 θ and find the equation of the tangent line at θ = π/3 .

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

A: Given curve is: y=6x cos x. We need to find tangent to y at (π, -6π)

Q: r = -1 + cos 0 0=t/2

A: In the question we have to find the slope of function -…

Q: What is the equation of the line tangent to the curve e" + cos(x) = 1 at the point (6,0)? A y = x -…

A: Given, The equation of the curve ey+cosx = 1 We have to find the equation of the line tangent at the…

Q: Find the equation of the tangent line to the curve (piriform) y^2 =x^3(7-x) at the point (2,√40) a…

A:

Q: What is the equation of the line tangent to the curve e + cos(x) =1 at the pointG.0) A (B) y=x+ C…

A:

Q: Given the graph of r sin 2y = y cos 2x pictured at right, what is the point-slope equation for the…

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: Find the equation of the tangent line to the curve y 3x cos x at the point (T, -37). || The equation…

A: Formula for finding the equation of a line having a slope of m and passing through the point (x1,y1)…

Q: Find the lengths of the curves y = sin -1x - √(1 - x2), 0≤ x ≤ 3/4

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

A: Given parametric equation is

Q: What is the equation of the line tangent to the curve e + cos(x) = 1 at the point ,0|? y=x+ y=0 TT…

A: Given that the curve is ey+cosx=1 and the point is π2,0. It is required to find the equation of…

Q: please help me with this

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

A: Given parametric equations are

Q: find the inflection point to the right of y-axis of the curve defined by the equation, y=x^2/2 +…

A: Given problem :- find the inflection point to the right of y-axis of the curve defined by the…

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=2 sint, y=3cost, 0st<27

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Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 = klo

A: Polar curve

Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Use the guidelines of this section to sketch the curve   y =sin x /( 2 + cos x )

A: Given: y=sinx2+cosx graph of given function can be drawn as below

Q: x = sin1/2? ,    y = cos1/2? ,    −? ≤ ? ≤ ?  Eliminate the parameter to find a Cartesian equation…

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Q: Find the equation of the line tangent to the graph of y = tan t at t = π/4.

A: Given that, the function of the graph  y = tan t at t = π/4   To find the equation of the line…

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: The equation for the tangent to the curve y = t+ at the point (1,3

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: 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: 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: What is the equation of the line tangent to the curve e+ cos(x) =1 at the point .0)? A y=0 B y=x -…

A: Explained below

Q: Find the equation of the line tangent to y = sin(x) going through 4

A: Given, y=sinx                 ...(1) At x=π4 Put x=π4 in equation (1) y=sinπ4y=22 Thus, the pointπ4,…

Q: Find the Cartesian equation of the curve: x = 2cos(theta) y = 1 + sin(theta) where theta is…

A: Given that the equation of the curve, x=2cosθy=1+sinθWhere,  0≤θ&lt;π2

Q: Use the guidelines of this section to sketch the curve   y =sin x /( 1 + cos x )

A: Consider the curves: y=sinx1+cosx

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

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.