Question

What is the amplitude and period of `y=2sinx`?

Answer 1

`2,2pi`

Explanation:

`"the standard form of the "color(blue)"sine function"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))`

`"where amplitude "=|a|," period "=(2pi)/b`

`"phase shift "=-c/b" and vertical shift "=d`

`"here "a=2,b=1,c=d=0`

`rArr"amplitude "=|2|=2," period "=2pi`

Answer 2

amplitude: `2`
period: `360^@`

Explanation:

the amplitude of `y = sin x` is `1`.

`(sin x)` is multiplied by `2`, i.e. after the function `sin x` has been applied, the result is multiplied by `2`.

the result of `sin x` for the graph `y = sinx` is `y` at any point on the graph.

the result of `2 sin x` for the graph `y = sin x` would be `2y` at any point on the graph.

since `y` is the vertical axis, changing the coefficient of `(sin x)` changes the vertical height of the graph.

the amplitude is the value of the distance between the `x`-axis and the highest or lowest point on the graph.

for `y = (1) sin x`, the amplitude is `1`.

for `y = 2 sin x`, the amplitude is `2`.

the period of a graph is how often the graph repeats itself.

the graph of `y = sin x` will repeat its pattern every `360^@`. `sin 0^@ = sin 360^@ = 1`, `sin 270^@ = sin 630^@ = -1`, etc.

(the graph shown is `y = sin x` where `0^@<=x<=720^@`)

if the value that the function `sin` is being applied to changes, the graph will change along the `x`-axis.

e.g. if the value is changed to `y = sin 2x`, `y` will be `sin 90^@` at `x = 45^@`, and `sin 360^@` at `x = 180^@`.

the range of the values that `y` can take will stay the same, but they will be at different points of `x`.

if the coefficient of `x` is increased, the highest and lowest points on the graph will seem closer together.

however, the function in question does not the coefficient of `(x)` - only the coefficient of `(sin x)`.

the range of values that `y` can take is doubled, but `x` will repeat itself at the same points.

the amplitude is `2`, and the period is `360^@`.