What is the period of #sin (5*x)#?

1 Answer
Johnson Z.
Jan 30, 2016

period#=72^@#

Explanation:

The general equation for a sine function is:

#f(x)=asin[k(x-d)]+c#

where:
#|a|=#amplitude
#|k|=#horizontal stretch/compression or #360^@/"period"#
#d=#phase shift
#c=#vertical translation

In this case, the value of #k# is #5#. To find the period, use the formula, #k=360^@/"period"#:

#k=360^@/"period"#

#5=360^@/"period"#

#5*"period"=360^@#

#"period"=360^@/5#

#"period"=72^@#

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

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