The parametric equations and describe a curve for

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

Problem

The parametric equations x=sin⁡tx=\sin t and y=cos⁡ty=\cos t describe a curve for 0≤t≤π0\le t\le\pi. What is the equation of the line tangent to the curve at t=π/3t=\pi/3? (a) y−12=−32(x−32)y-\dfrac12 = -\dfrac{\sqrt{3}}{2}\left(x-\dfrac{\sqrt{3}}2\right) (b) y−32=−3(x−12)y-\dfrac{\sqrt{3}}2 = -\sqrt{3}\left(x-\dfrac12\right) (c) y−12=−3(x−32)y-\dfrac12 = -\sqrt{3}\left(x-\dfrac{\sqrt{3}}2\right) (d) y−12=3(x−32)y-\dfrac12 = \sqrt{3}\left(x-\dfrac{\sqrt{3}}2\right)

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