find the amplitude, period, horizontal shift and vertical shift for the following equation.\ny = - cos(2x…

Explanation:

Step1: Recall amplitude formula

For $y = A\cos(Bx - C)+D$, amplitude is $|A|$. Here $A=- 1$, so amplitude $=| - 1|$.

Step2: Recall period formula

The period of $y = A\cos(Bx - C)+D$ is $\frac{2\pi}{|B|}$. Here $B = 2$, so period $=\frac{2\pi}{2}$.

Step3: Recall horizontal - shift formula

The horizontal shift of $y = A\cos(Bx - C)+D$ is $\frac{C}{B}$. Here $C=\frac{2\pi}{3}$ and $B = 2$, so horizontal shift $=\frac{\frac{2\pi}{3}}{2}$.

Step4: Recall vertical - shift formula

For $y = A\cos(Bx - C)+D$, the vertical shift is $D$. Here $D = 2$.

Answer:

Amplitude = $1$ Period = $1$ Horz. Shift = $\frac{\pi}{3}$ Vert. Shift = $2$