The curve is defined by and for

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The curve is defined by

x=\sin t

and

y=\cos t

for

0<t<\pi

. The tangent line at

t=\pi/4

is perpendicular to the tangent line at which of the following parameter values? (a)

\dfrac{\pi}{2}

(b)

\dfrac{3\pi}{4}

(c)

\dfrac{\pi}{6}

(d)

\dfrac{5\pi}{6}

Related theory

Parametric Functions
Implicit and parametric differentiation
Derivatives of parametric functions
Continuity and Differentiability

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