Question

which of the following could be found in a table of values for the function ( g(x)=cos (-1.5 x)-1 ) ? (1 point)
( \bigcircleft(\frac{2 pi}{3}, 0
ight) )
( \bigcircleft(\frac{2 pi}{3},-2
ight) )
( \bigcircleft(\frac{2 pi}{3},-1
ight) )
( \bigcirc ) there is no viable option provided.

Explanation:

Step1: Simplify the function

Since $\cos(-\alpha)=\cos\alpha$, then $g(x)=\cos(1.5x)-1$.

Step2: Substitute $x = \frac{2\pi}{3}$ into the function

We have $1.5x=1.5\times\frac{2\pi}{3}=\pi$.
Then $g(\frac{2\pi}{3})=\cos(\pi)-1$.
Since $\cos(\pi)=-1$, so $g(\frac{2\pi}{3})=-1 - 1=-2$.

Answer:

$(\frac{2\pi}{3},-2)$