What is the period, amplitude, and frequency for the graph $f (x) = 1 + 2 sin (2 (x + π))$ $f(x) = 1 + 2 \sin(2(x + \pi))$ ?

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What is the period, amplitude, and frequency for the graph $f (x) = 1 + 2 sin (2 (x + π))$ $f(x) = 1 + 2 \sin(2(x + \pi))$ ?

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Answer 1 · 2014-12-06T20:29:00

The general form of the sine function can be written as

$f (x) = A sin (B x \pm C) \pm D$ $f(x) = A sin(Bx +- C) +- D$ , where

$| A |$ $|A|$ - amplitude;
$B$ $B$ - cycles from $0$ $0$ to $2 π$ $2pi$ - the period is equal to $\frac{2 π}{B}$ $(2pi)/B$
$C$ $C$ - horizontal shift;
$D$ $D$ - vertical shift

Now, let's arrange your equation to better match the general form:

$f (x) = 2 sin (2 x + 2 π) + 1$ $f(x) = 2 sin(2x +2pi) +1$ . We can now see that

Amplitude - $A$ $A$ - is equal to $2$ $2$ , period - $B$ $B$ - is equal to $\frac{2 π}{2}$ $(2pi)/2$ = $π$ $pi$ , and frequency, which is defined as $\frac{1}{p e r i o d}$ $1/(period)$ , is equal to $\frac{1}{π}$ $1/(pi)$ .

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What is the period, amplitude, and frequency for the graph $f (x) = 1 + 2 sin (2 (x + π))$ $f(x) = 1 + 2 \sin(2(x + \pi))$ ?

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Science

Math

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What is the period, amplitude, and frequency for the graph f(x)=1+2sin(2(x+π))f(x) = 1 + 2 \sin(2(x + \pi))?

1 Answer

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What is the period, amplitude, and frequency for the graph $f (x) = 1 + 2 sin (2 (x + π))$ $f(x) = 1 + 2 \sin(2(x + \pi))$ ?