home > s25 ma2090 - dambroise precalculus > assessment\nhomework #14 - graphs of sine, cosine…

Explanation:

Step1: Identify key - points

The cosine function $y = \cos(x)$ has a period of $2\pi$. At $x = 0$, $\cos(0)=1$; at $x=\frac{\pi}{2}$, $\cos(\frac{\pi}{2}) = 0$; at $x=\pi$, $\cos(\pi)= - 1$; at $x=\frac{3\pi}{2}$, $\cos(\frac{3\pi}{2}) = 0$; at $x = 2\pi$, $\cos(2\pi)=1$.

Step2: Plot key - points

Plot the points $(0,1),(\frac{\pi}{2},0),(\pi, - 1),(\frac{3\pi}{2},0),(2\pi,1)$ on the given grid.

Step3: Draw the curve

Connect the points with a smooth curve. The curve is symmetric about the y - axis and oscillates between $y=-1$ and $y = 1$.

Answer:

Sketch a curve that passes through the points $(0,1),(\frac{\pi}{2},0),(\pi, - 1),(\frac{3\pi}{2},0),(2\pi,1)$ and is symmetric about the y - axis, oscillating between $y=-1$ and $y = 1$.