For a particle

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For a particle, the velocity components are

\dfrac{dx}{dt}=\cos\bigl(t+\tfrac{\pi}{4}\bigr)

and

\dfrac{dy}{dt}=\sin\bigl(t+\tfrac{\pi}{4}\bigr)

. At time

t=-\tfrac{\pi}{4}

the particle is located at

(2,0)

. Determine the parametric equations

x(t)

and

y(t)

valid for all real

t