The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is...

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is a cycloid.

(a) Find the slope of the tangent line to the cycloid for 0 < t < 2π.

dy

dx

(b) Find an equation of the tangent line to the cycloid at t =

π

3

(c) Find the length of the cycloid from t = 0 to t =

π

2

Expert Solution

milcah answered 3 years ago

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π...

Consider the parametric equation of a curve: x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π Part (a): Find the Cartesian equation of the curve by eliminating the parameter. Also, graph the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. Label any x and y intercepts. Part(b): Find the point (x,y) on the curve with tangent slope 1 and write the equation of the tangent line.

Convert x=cos(3t)+sin(3t) & y=cos(t)-sin(t) into an equation of x-y form (cartesian equation). Thank you

a. (5 Marks) 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) =...

a. 1 1 cos(x)cos(y) = -cos(x-y) + -cos(x + y) 1 l sin(x)sin(y) = -cos(x-y)--cos(x+ y) 1 l sin(x)cos(y) =—sin(x-y) +-sin(x + y) A DSB-FC (double sideband-full carrier) signal s(t) is given by, s(t) = n cos(2rr/cf)+ cos(2«-/mt)cos(2«-fct) What is the numeric value for the AM index of modulation, m, fors(f) ?

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line...

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line to curve when t=1

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos...

The cycloid has parametric equations x = a(t + sin t), y = a(1 - cos t). Find the length of the arc from t = 0 to t = pi. [ Hint: 1 + cosA = 2 cos2 A/2 ]. and the arc length of a parametric

y''(t)+(x+y)^2y(t)=sin(xt+yt)-sin(xt-y*t), y(0)=0, y'(0)=0, x and y are real numbers

y''(t)+(x+y)^2*y(t)=sin(x*t+y*t)-sin(x*t-y*t), y(0)=0, y'(0)=0, x and y are real numbers

3. Consider the parametric curve x = sin 2t, y = − cos 2t for −π/4...

3. Consider the parametric curve x = sin 2t, y = − cos 2t for −π/4 ≤ t ≤ π/4. (a) (2 pts) Find the Cartesian form of the curve. (b) (3 pts) Sketch the curve. Label the starting point and ending point, and draw an arrow on the curve to indicate the direction of travel. (c) (5 pts) Find an equation for the curve’s tangent line at the point √2/2, −√2/2 .

Determine the solutions for y = y(x) for the differential equation cos x − x sin x...

Determine the solutions for y = y(x) for the differential equation cos x − x sin x + y 2 + 2 x y dy/dx= 0.

How does the graph of y = sin x compare with the graph of y = cos x? Explain how you could horizontally translate the graph of y = sin x to obtain y = cos x.

Problem 7. Consider the line integral Z C y sin x dx − cos x dy....

Problem 7. Consider the line integral Z C y sin x dx − cos x dy. (Please show all work) a. Evaluate the line integral, assuming C is the line segment from (0, 1) to (π, −1). b. Show that the vector field F = is conservative, and find a potential function V (x, y). c. Evaluate the line integral where C is any path from (π, −1) to (0, 1).

Question