Let and be positive constants

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

Problem

Let

a

and

k

be positive constants. A curve is described by

x=a\cos t+kt

and

y=a\sin t+k

for real

t

. (i) Derive an expression for

\dfrac{dy}{dx}

in terms of

t

a

and

k

. (ii) Hence find the condition on

t

for which the tangent to the curve is horizontal. (iii) If

a=4

and

k=1

, evaluate the slope of the tangent at

t=\dfrac{\pi}{3}