graph the function (f(x)=-sin(x)).
graph the function (f(x)=-sin(x)).
Answer
Explanation:
Step1: Recall properties of y = sin(x)
The function y = sin(x) has a period of (2\pi), amplitude of 1, and passes through points ((0,0)), ((\frac{\pi}{2},1)), ((\pi,0)), ((\frac{3\pi}{2}, - 1)), ((2\pi,0)) etc.
Step2: Analyze y=-sin(x)
The negative sign in (y =-\sin(x)) reflects the graph of (y=\sin(x)) about the x - axis. So the points for (y =-\sin(x)) are ((0,0)), ((\frac{\pi}{2},-1)), ((\pi,0)), ((\frac{3\pi}{2},1)), ((2\pi,0)) etc.
Step3: Plot the points
Plot the key - points ((0,0)), ((\frac{\pi}{2},-1)), ((\pi,0)), ((\frac{3\pi}{2},1)), ((2\pi,0)) on the given coordinate grid and then draw a smooth curve passing through these points with a period of (2\pi).
Answer:
Graph the points ((0,0)), ((\frac{\pi}{2},-1)), ((\pi,0)), ((\frac{3\pi}{2},1)), ((2\pi,0)) and draw a smooth sine - like curve with period (2\pi) that is a reflection of (y = \sin(x)) about the x - axis.