Mathematics

Mathematics

Problem

For the parametric curve x=t−sin⁡t,  y=1−cos⁡tx = t - \sin t,\; y = 1 - \cos t with 0<t<2π0 < t < 2\pi, the slope of the tangent equals 12\dfrac{1}{2} at which of the following values of tt? a) t=π−2tan⁡−12t = \pi - 2\tan^{-1}2 b) t=tan⁡−12t = \tan^{-1} 2 c) t=2tan⁡−12t = 2\tan^{-1} 2 d) t=2tan⁡−1 ⁣(12)t = 2\tan^{-1}\!\bigl(\tfrac{1}{2}\bigr)

Browse the problem library