What is the period of $sin (5 \cdot x)$ $sin (5*x)$ ?

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What is the period of $sin (5 \cdot x)$ $sin (5*x)$ ?

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Answer 1 · 2016-01-30T17:45:49

period $= 72^{\circ}$ $=72^@$

Explanation:

The general equation for a sine function is:

$f (x) = a sin [k (x - d)] + c$ $f(x)=asin[k(x-d)]+c$

where:
$| a | =$ $|a|=$ amplitude
$| k | =$ $|k|=$ horizontal stretch/compression or $\frac{360^{\circ}}{period}$ $360^@/"period"$
$d =$ $d=$ phase shift
$c =$ $c=$ vertical translation

In this case, the value of $k$ $k$ is $5$ $5$ . To find the period, use the formula, $k = \frac{360^{\circ}}{period}$ $k=360^@/"period"$ :

$k = \frac{360^{\circ}}{period}$ $k=360^@/"period"$

$5 = \frac{360^{\circ}}{period}$ $5=360^@/"period"$

$5 \cdot period = 360^{\circ}$ $5*"period"=360^@$

$period = \frac{360^{\circ}}{5}$ $"period"=360^@/5$

$period = 72^{\circ}$ $"period"=72^@$

$:.$ , the period is $72^@$ .

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