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

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 the Cartesian equation of the curve: [2r/r2 = 1+ cos a]

A:

Q: Consider the following. x = sin(t),    y = csc(t),    0 < t < π/2 (a) Eliminate the…

A: x(t) = sin(t)y(t) =csc(t)

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

A:

Q: The curve ver = V1 + sin20.

A: Solution :-

Q: - Find dx2 for the curve defined by parametric equations x = t³ and y = e'.

A: Differentiate given parametric equation

Q: A curve is defined by the parametric equations a(t) = 2 cos(5t) and y(t) = -7 sin(-10t). Find .

A:

Q: Find the equation of the tangent line to the curve y = 6 sin a at the point (, 3). The equation of…

A:

Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: Given this pair of parametric equations and value of t, x = Vt, y = at t = 4 a) Find the point…

A: To solve this put t=u and then solve it Here we are going to use formula of differention of tn…

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

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: Find parametric equations for the given curve. y = 4x2 - x

A: The given curve is y = 4x2 - x

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 parametric equation of a curve: x(θ) = sin θ − 1 and y(θ) = θ + cosθ a. Find dy/dx b. Find…

A: Given that  x(θ) = sin θ − 1 and y(θ) = θ + cosθ To determine the  Find dy/dx b. Find d2y/dx2   c.…

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: :2 cos(t) y = 3 sin(t) T = Find the slope of the tangent line to the parametric curve at the point 4

A:

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: Find dy/dx and d2 y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Given, x = cos3 θ, y = sin3 θ Parameter θ = π/4

Q: X= 4 cos(t) , y= 5 sin(t) find rectangular coordinates equation for the curve by eliminating the…

A:

Q: Find the exact slope of the tangent line to the parametric curve at the point where y = 2 sin(t) t =…

A: x=8 cos (t) y=2 sin (t)

Q: Sketch the curve y=sin(x)/(1+cos(x)).

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 2 cos(t) T at the point 4 Find the slope of the tangent line to the parametric curve ly = 1 sin(t)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

A:

Q: please help me with this

A:

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 length of the curve y = ln (sin x),  pai/6&lt;=x&lt;=pai/2.

A: The given curve is,

Q: x = 1– t- t - te [-2,2] y =t – t3

A:

Q: Given the parametric curve x = t – sin(t),y = 1 - cos (t), find an equation for the line tangent to…

A: Given: x=t-sint y=1-cost at t=pi/3

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

A:

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 the equation of the tangent line to the curve y 8 sin r at the point The equation of this…

A: Given query is to find the equation of tangent line. Since slope of  tangent is given by derivative…

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

A:

Q: 5. Determine the slope of the tangent line, the the equation of the tangent line, and the concavity…

A: this is the equation of tangent line.

Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…

A:

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

A:

Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

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: A parametric curve has the equations x =t+sin t and y= cos t. Calculate and , both evaluated at t=…

A: Use dy/dx= (dy/dt)/(dx/dt)

Q: A curve is described parametrically as x = e' sint, y = e'cost, – o <t< ao. Find the equation of the…

A:

Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

A:

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

A:

Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: (a) The curve with equation y? = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the…

A: To determine the equation of tangent line.

Q: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

A:

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

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.