Question

graph each function.

$f\left(x\right)=\left\{\begin{array}{ll}\sin x& 0\le x<\frac{5\mathrm{\pi }}{4}\\ \cos x& \frac{5\mathrm{\pi }}{4}\le x\le 2\mathrm{\pi }\end{array}\right.$

Short answer

The graph of the function$f\left(x\right)=\left\{\begin{array}{ll}\sin x& 0\le x<\frac{5\mathrm{\pi }}{4}\\ \cos x& \frac{5\mathrm{\pi }}{4}\le x\le 2\mathrm{\pi }\end{array}\right.$ is

Step-by-step solution

Step 1. Given data

The given function is

$f\left(x\right)=\left\{\begin{array}{ll}\sin x& 0\le x<\frac{5\mathrm{\pi }}{4}\\ \cos x& \frac{5\mathrm{\pi }}{4}\le x\le 2\mathrm{\pi }\end{array}\right.$

Step 2. Points of function

Determine coordinate of the points of the function $f\left(x\right)=\sin x$in the interval$0\le x<\frac{5\mathrm{\pi }}{4}$

Step 3. Points of the function

Determine the coordinate of points of the function $f\left(x\right)=\cos$in the interval$\frac{5\mathrm{\pi }}{4}\le x\le 2\mathrm{\pi }$

Step 4. Graph of the function

Locate the points and connect them to plot the graph of$f\left(x\right)=\left\{\begin{array}{ll}\sin x& 0\le x<\frac{5\mathrm{\pi }}{4}\\ \cos x& \frac{5\mathrm{\pi }}{4}\le x\le 2\mathrm{\pi }\end{array}\right.$