Question

What is the amplitude and period of f(t)=-cos t

Answer 1

c. amplitude:
`\displaystyle 1;`period:
`\displaystyle 2\pi`

Explanation:

`\displaystyle f(t) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow (C)/(B) \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow (2)/(B)\pi \hookrightarrow \boxed{2\pi} \hookrightarrow (2)/(1)\pi \\ Amplitude \hookrightarrow 1`

With the above information, you now should have an idea of how to interpret graphs like this.

I am joyous to assist you at any time.

Answer 2

c. amplitude: 1; period:
`2\pi`

Explanation:

The given function is
`f(t)=- \cos t`

This function is of the form;

`y=A \cos Bt`

where
`|A|` is the amplitude.

When we compare
`f(t)=- \cos t` to
`y=A \cos Bt`, we have

`A=-1`, therefore the amplitude of the given cosine function is
`|-1|=1`

The period is given by;

`T=(2\pi)/(|B|)`

Since B=1, the period is
`T=(2\pi)/(|1|)=2\pi`