Max/min with trig funtions problem

[icosane]

Homework Statement

Within the interval ( -22.27, 40.55 ), for what value of x does f(x) take on a minimum if
f(x)=4.7sin(0.1x)−6.1cos(0.1x)

Later the question asks for the maximum as well.

2. The attempt at a solution

I know to find the critical values to take the first derivative and set it equal to zero, then solve for x. When I do that I get the equation...

0=.47cos(.1x)+.61sin(.1x)

When I solve this guy, by manipulating the equation to get tan(.1x)=-.47/.61, I get only one value, x=-6.56487, which is the minimum value. But I also need a maximum value. I've tried both end points within the interval and they were wrong. Is there something I'm missing here?

Any help would be appreciated.

 

[CompuChip]

The tangent is a periodic function.
What is the period of tan(0.1 x)?
One period beyond x = -6.5... there will be another solution which is also in the given interval.