Question 1195467
<br>
A general form of a tangent function is<br>
{{{y=a*tan(b(x-c))+d}}}<br>
a determines the steepness of the graph
the period is (pi)/b
c is the phase (horizontal) shift
d is the vertical shift<br>
This problem puts no requirement on the steepness of the graph or the vertical shift, so we can let a=1 and d=0, giving us<br>
{{{y=tan(b(x-c))}}}<br>
This problem says the period should be 3pi, so<br>
{{{pi/b=3pi}}}
{{{b=(pi)/(3pi)=1/3}}}<br>
And the phase shift is given as pi/2.<br>
So b=1/3 and c=pi/2:<br>
ANSWER: {{{y=tan((1/3)(x-pi/2))}}}<br>
That can be written in many forms; for example,<br>
{{{y=tan((1/3)x-(pi/6))}}}<br>