Question

The following is the graph of f(x) = sin (x-180 degrees) -1

True
False

Answer 1

True

Explanation:

Check the values of
`f(x)` at
`x=0,\pm0.5\pi,\pm\pi,\pm1.5\pi,\pm2\pi`

`x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f(x)\\0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0-180)-1=-1\\0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(0.5\pi-180)-1=-2\\\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(\pi-180)-1=-1\\1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(1.5\pi-180)-1=0\\2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(2\pi-180)-1=-1\\-0.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-0.5\pi-180)-1=0\\-\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-\pi-180)-1=-1\\\\`

`-1.5\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-1.5\pi-180)-1=-2\\-2\pi \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sin(-2\pi-180)-1=-1`

Each
`(x,y)` point is on the graph.

Hence graph represents the given function.