What is the period of the function $y = 3 sin (2 x)$ $y=3 sin(2x)$ ?

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What is the period of the function $y = 3 sin (2 x)$ $y=3 sin(2x)$ ?

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Answer 1 · 2016-12-29T03:33:07

The period is $π$ $pi$ .

Explanation:

Given a trig function in the form $y = A sin (B x - C) + D$ $y=Asin(Bx-C)+D$ .

the period is equal to $\frac{2 π}{B}$ $(2pi)/B$ .

In this example, $y = 3 sin 2 x$ $y=3sincolor(red)2x$ , $B = 2$ $B=color(red)2$

The period is equal to $\frac{2 π}{2} = π$ $(2pi)/color(red)2 =pi$ .

Another way to think of this is by examing the function $y = sin x$ $y=sinx$ , which has a period of $2 π$ $2pi$ . In other words, once complete cyle of sin is $2 π$ $2pi$ "long".

In comparison, $y = sin 2 x$ $y=sincolor(red)2x$ has a period of $π$ $pi$ , and $2$ $color(red)2$ complete cycles "fit" within $2 π$ $2pi$ , making one cycle $π$ $pi$ "long".

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What is the period of the function $y = 3 sin (2 x)$ $y=3 sin(2x)$ ?

1 Answer

Explanation:

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What is the period of the function y=3sin(2x)y=3 sin(2x)?

1 Answer

Explanation:

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What is the period of the function $y = 3 sin (2 x)$ $y=3 sin(2x)$ ?