Question 29987
For the form y=asin(bx+c)+d
The period is 2(pi)/b
In your 1st equation b=c so the period is 2(pi)/3
2nd equation has b=1/4 so period is 2(pi)/(1/4)=8(pi)
Domain of tanx:  tanx=(sinx)/(cosx); this is undefined if cosx=0
which happens if x=90 degrees or x=270 degrees.
Domain of the tanx is all real numbers except 90+-180n where n is
0,1,2,...etc.

Cheers,
Stan H.