Whats the equation for a sine function with a period of 3/7, in radians?

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Answer 1 · 2018-04-14T11:55:59

#color(blue)(f(x)=sin((14pi)/3x))#

We can express trigonometric functions in the following way:

#y=asin(bx+c)+d#

Where:

# \ \ \ \bbacolor(white)(8888) " is the amplitude"#.

#bb((2pi)/b) color(white)(8..)" is the period"#

#bb((-c)/b)color(white)(8..) " is the phase shift"#.

# \ \ \ bbdcolor(white)(8888) " is the vertical shift"#.

Note:

#bb(2picolor(white)(8) "is the period of "sin(theta))#

We require a period of:

#3/7# , so we use:

#(2pi)/b=3/7#

#b=(14pi)/3#

So we have:

#a = 1#

#b=(14pi)/3#

#c=0#

#d=0#

And the function is:

#color(blue)(f(x)=sin((14pi)/3x))#

The graph of #f(x)=sin((14pi)/3x)# confirms this:

enter image source here