Question

Write an equation for a cosine function with the

Answer 1

Answer:

The required function is $f(x)=2\cos (\frac{\pi}{3}x-\frac{2\pi}{3})$.

Step-by-step explanation:

Note: The value of period and phase shift are not given properly.

Consider amplitude = 2, period = 6, phase shift = 2.

The general form of cosine function is

$f(x)=A\cos (Bx-C)+D$                ..... (1)

where, |A| is amplitude, $\frac{2\pi}{B}$ is period, C/B is phase shift and D is midline.

From the given information we conclude that

$|A|=2$

$\frac{2\pi}{B}=6$

$\frac{2\pi}{6}=B$

$\frac{\pi}{3}=B$

$\text{Phase shift}=\frac{C}{B}$

$\text{Phase shift}\times B=C$

$2\times \frac{\pi}{3}=C$

$\frac{2\pi}{3}=C$

Substitute A=2, $B=\frac{\pi}{3}$ and $C=\frac{2\pi}{3}$ and D=0 in equation (1).

$f(x)=2\cos (\frac{\pi}{3}x-\frac{2\pi}{3})+0$

$f(x)=2\cos (\frac{\pi}{3}x-\frac{2\pi}{3})$

Therefore, the required function is $f(x)=2\cos (\frac{\pi}{3}x-\frac{2\pi}{3})$.