Mathematics

Mathematics

Problem

Consider the parametric equations x(t)=sin⁡tx(t)=\sin t and y(t)=cos⁡2ty(t)=\cos 2t for 0<t<2π0<t<2\pi. Over which of the following intervals of tt is the curve concave up with respect to xx ? a) 0<t<π2 and 3π2<t<2π0<t<\dfrac{\pi}{2}\text{ and }\dfrac{3\pi}{2}<t<2\pi b) The curve is never concave up on 0<t<2π0<t<2\pi c) π2<t<3π2\dfrac{\pi}{2}<t<\dfrac{3\pi}{2} d) All tt in 0<t<2π0<t<2\pi except t=π2, 3π2t=\dfrac{\pi}{2},\,\dfrac{3\pi}{2}

Browse the problem library