graph the function f(x) = sin(x) - 2.

graph the function f(x) = sin(x) - 2.

graph the function f(x) = sin(x) - 2.

Answer

Answer:

To graph $y = \sin(x)-2$, we can use the following steps to plot key - points and draw the curve:

  1. Recall the properties of the basic sine function $y = \sin(x)$. The amplitude of $y=\sin(x)$ is $A = 1$, the period is $T=2\pi$, and the range is $[- 1,1]$.
  2. For the function $y=\sin(x)-2$, it is a vertical shift of the function $y = \sin(x)$ down by 2 units.
  3. Find the key - points:
    • When $x = 0$, $y=\sin(0)-2=0 - 2=-2$.
    • When $x=\frac{\pi}{2}$, $y=\sin(\frac{\pi}{2})-2=1 - 2=-1$.
    • When $x=\pi$, $y=\sin(\pi)-2=0 - 2=-2$.
    • When $x=\frac{3\pi}{2}$, $y=\sin(\frac{3\pi}{2})-2=-1 - 2=-3$.
    • When $x = 2\pi$, $y=\sin(2\pi)-2=0 - 2=-2$.
  4. Plot these key - points on the coordinate plane and connect them with a smooth curve. The period of $y=\sin(x)-2$ is still $2\pi$, and the range is $[-3,-1]$.

Explanation:

Step1: Recall basic sine function

The basic $\sin(x)$ has amplitude 1, period $2\pi$.

Step2: Identify vertical shift

The $-2$ shifts $\sin(x)$ down 2 units.

Step3: Calculate key - points

Evaluate $y=\sin(x)-2$ at $x = 0,\frac{\pi}{2},\pi,\frac{3\pi}{2},2\pi$.

Step4: Plot and draw

Plot points and draw a smooth sine - like curve.