How do you solve these? please help. I need to find the period and I am so lost! Y= cot2 (x) Thank you!

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Answer 1 · 2018-02-20T03:16:36

For the first function #\ \ \ ##y=cot[2(x)]##\ \ \ #

#\text{Period}=\frac{\pi }{2}#

Consider the general form of periodic function:

#y\ =\ a\cot (bx\pm c)\pm d#

The period of a periodic function can be calculated by the formula:

#\text{Period}\ =\ \frac{\text{periodicity of base}}{|b|}#

We know that the periodicity of the #sin(x)#, #cos(x)#, #csc(x)# and #sec(x)# is #2pi# while that of #tan(x)# and #cot(x)# is #pi#.

So, for our given function #y=cot[2(x)]#, we have:

#a=1#, #b=2#, #c=0# and #d=0#

So, the required period of this function is:

#\text{Period}=\frac{\pi }{|2|}#

#=\frac{\pi }{2}#

Try others by yourself. They are not that hard!