1.) Plot the parametric equations below. x=6 cos(t) y=4 sin(t) 2). Write the par
ID: 2862286 • Letter: 1
Question
1.) Plot the parametric equations below.
x=6 cos(t)
y=4 sin(t)
2). Write the parametric equations below in Cartesian coordinates.
x=3 cos(t)
y=4 sin(t)
3).Given the parametric equations x = f(t) and y = g(t), dy/dx is given by g'(t)/f'(t). Find dy/dx given parametric equations below.
dy/dx=(g^? (t))/(f^? (t) )
Parametric equations:
x=(t+1)/2
y=-t^2+t
4). Convert the following polar equation to Cartesian coordinates.
r=8 sin(?)
5). Find the slope of the line tangent to the polar curve at the point given point.
r=4+sin(?);(4, 0)
Explanation / Answer
3 -
x = (t + 1)/2
=> x = (1/2)t + 1/2
=> dx/dt = d/dt((1/2)t + 1/2)
=> dx/dt = d/dt((1/2)t) + d/dt(1/2)
=> dx/dt = 1/2 + 0
=> dx/dt = 1/2
=> dt/dx = 2
y = -t^2 + t
=> dy/dt = d/dt(-t^2 + t)
=> dy/dt = d/dt(-t^2) + d/dt(t)
=. dy/dt = -2t + 1
dy/dx = dy/dt * dt/dx
=> dy/dx = (-2t + 1) * 2
=> dy/dx = -4t + 2
edit your hint is the same thing as dy/dx = (dy/dt)/(dx/dt)
=> dy/dx = (-2t + 1) / (1/2)
=> dy/dx = (-2t + 1) * 2
=> dy/dx = -4t + 2
4 -
r = 8 sin ? or
r
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