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Derivatives help please?

0 votes
Differentiate with respect to t the following equations

X(t)=3cos(pi*t)

Y(t)=5sin(pi*t)
asked Jan 2, 2013 in CALCULUS by chrisgirl Apprentice

1 Answer

+2 votes
X(t)=3cos(pi*t)------------(1);Y(t)=5sin(pi*t)-----------(2)

Differentiate equation (1) with respect  to  "t"

 dx/dt  =d/dt 3 cos (pi*t)

 dx/dt = 3(-sin (pi*t) *d/dt (pi*t)

 dx/dt =-3sin(pi*t)*(pi)

 dx/dt =-3(pi)sin (pi*t)------------(a)

Differentiate equation (2) with respect  to  "t"

dy/dt =5 d/dt sin (pi*t)

dy/dt = 5cos(pi*t) *d/dt (pi*t)

dy/dt = 5cos(pi*t)(pi)

dy/dt = 5(pi)cos(pi*t)--------(b)

(a) / (b)

dy / dt / dx / dt  = 5(pi)cos(pi*t) /  -3 (pi)sin(pi*t)

dy/dx = -5 / 3 ( cos(pi*t)  / sin(pi*t)

dy/dx = -5 / 3(cot(pi*t)
answered Jan 2, 2013 by ricky Pupil

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