The curve is given by and

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

Problem

The curve is given by

x=t+\sin t

and

y=t+\cos t

. (i) Determine all values of

t

0< t<2\pi

for which the slope of the tangent is

\dfrac12

. (ii) Write the equation of the tangent at the smallest positive such value of

t