over which interval is the graph of y = cos(x) strictly increasing?\n0 < x < \\frac{\\pi}{2}\n0 < x <…

over which interval is the graph of y = cos(x) strictly increasing?\n0 < x < \\frac{\\pi}{2}\n0 < x < \\pi\n\\frac{\\pi}{2} < x < \\frac{3\\pi}{2}\n\\pi < x < 2\\pi

over which interval is the graph of y = cos(x) strictly increasing?\n0 < x < \\frac{\\pi}{2}\n0 < x < \\pi\n\\frac{\\pi}{2} < x < \\frac{3\\pi}{2}\n\\pi < x < 2\\pi

Answer

Explanation:

Step1: Recall cosine function property

The cosine function $y = \cos(x)$ has a period of $2\pi$. Its derivative $y'=-\sin(x)$. The function is increasing when $y'> 0$, i.e., $-\sin(x)>0$ or $\sin(x)<0$.

Step2: Analyze sine - function sign

The sine function $\sin(x)<0$ in the interval $(\pi, 2\pi)$.

Answer:

$\pi<x<2\pi$