6. A parametric equation is given by x=1.5 sin (5t), y-1.5 cos (3t), Plot the function for 0

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

A: We are given the parametric equations: x=6cosθy=6sinθ We know that the derivative of  cosa=-sina and…

Q: The parametric equations for the paths of two objects are given. At what rateis the distance between…

A: Given: The parametric equations for the paths of two objects are given. At what rateis the distance…

Q: Find parametric equations for line that is tangent to the curve x=cost, y=sint, z=t at the point…

A:

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

A: The answer is found in step-2

Q: 18. Find the second derivative of y with respect to x of the following parametric equations. x = 1 +…

A: Using derivatives of parametric equations.

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations x…

A: Given: x=4 costy=2 sin2tt=π3

Q: Consider the parametric equations x = 2t – 5, y = 6. dy Use the derivative formula from Section 10.2…

A:

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

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

A:

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: Given this pair of parametric equations and interval for t, x=t+sint, y=cos(2t), 0 ≤t ≤2 (A) write…

A: The parametric equations are x=t+sint, y=cos2t and t∈0,2π.

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

A:

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

A:

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

A: To find the Cartesian equation of the given curve.

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

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

A:

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: 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: The parametric equation of the motion of a particle on a plane is given by 3/2. x = te + 2t12; y=t'…

A:

Q: what points does the curve described by the parametric equations x = 2a cos t – a cos 2t d y = 2a…

A:

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: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…

A:

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

A: The tangent line to a parametric curve given by c(t)=< x(t) , y(t) , z(t) > at some point…

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

A:

Q: The derivative I of the parametric equations and y=5vt is

A:

Q: of the points where the parametric equation y = 2 cost 0≤t≤ 2π will have vertical tangent. Determine…

A: Given is the parametric equation x=5sin2t , y=2cost   0≤t≤2π We have to find the point where the…

Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: The equation for the tanget to graph of y=sin^1(x/2) at the origin is

A: Given, y=sin1x2 Differentiate the given function with respect to x we get, dydx=cosx212 At point…

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: 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 t from the parametric equation x = 3 sint y = 3 cost 0 ≤t≤ 2π.

A:

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: 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: x = 2 cos(3t) – 4 sin( 3t) IT t = 2 y = 3 tan( 6t)

A: given,        x=2cos3t-4sin3t   and y =3tan6t

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

A: The derivative dydx defines the slope of the tangent drawn to the curve.

Q: Find all points of intersection of the curves r = sin 0, r= sin 20

A:

Q: Sketch the curve by using the parametric equation to plot points. Then, eliminate the parameter 0,…

A:

Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Please check step 2 for the solution.!

Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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: Find the second derivative of y with respect to x from the parametric equations given. x = 3 + 4…

A:

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

A:

Q: Given the parametric equation : X = sin t cos t and y = sin t where 0 < t < 2n a. What is the slope…

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.