Question

Determine the ........ of y= 4sin2x

o Amplitude
o Period
o Intercepts
o Maximum
o Minimum

Answer 1

Amplitude:
`A = 4`

Period:
`\tau = \pi`

Minimum: -4

Maximum: 4

Intercepts:
`x = (1)/(2)\cdot [0 \pm \pi \cdot n]`,
`\forall \,n\in \mathbb{N}_(O)`

Step-by-step explanation:

The expression described on statement is a sinusoidal formula, whose expression is of the form:

`y = A\cdot \sin \left((2\pi\cdot x)/(\tau)\right)` (1)

Where:

`x` - Independent variable.

`y` - Dependent variable.

`A` - Amplitude.

`\tau` - Period.

By direct comparison, we calculate the amplitude and period:

Amplitude

`A = 4`

Period

`(2\pi)/(\tau) = 2`

`\tau = \pi`

Minimum and Maximum

The sine is a bounded function between -1 and 1, meaning that sinusoidal formula is bounded between
`-A` and
`A`. Hence, the minimum and maximum are -4 and 4, respectively.

Intercepts

The intercepts are set of points of the sinusoidal formula such that
`y = 0`. The sine function is a periodic function which equals 0 each
`\pi` radians.

`4\cdot \sin 2x = 0`

`\sin 2x = 0`

`2\cdot x = \sin^(-1) 0`

`x = (1)/(2)\cdot \sin^(-1) 0`

`x = (1)/(2)\cdot [0 \pm \pi \cdot n]`,
`\forall \,n\in \mathbb{N}_(O)`