To start off, we need to know that 0 to pi/2 is 1st quadrant, pi/2 to pi is 2nd, pi to 3pi/2 is third and 3pi/2 to 2r is fourth quadrant. According to tangent and cotangent 1st quad is +, 2nd is -, 3rd is +, and 4th is -.
On the left is a cotangent graph and it goes downhill because cot=x/y and it has asymptotes when y=0 which is (1,0) and (-1,0). In degrees, those coordinates are 0 and 180 so there are asymptotes are at 0 and pi or -pi. So from 0 to pi/2, cotangent is positive in the 1st quadrant so that part of the graph hugs up the asymptotes. From pi/2 to r, cotangent is negative in the 2nd quadrant so that part of the graph hugs down the asymptote. after connecting the two, we see that cotangent graph goes downhill.
On the left again is a tangent graph and it goes uphill because tan=y/x and it has asymptotes when x=0 which is (0,1) and (0,-1). In degrees, those coordinates are 90° and 270° so their asymptotes are at +/-pi/2 or +/-3pi/2. So from 0 to pi/2,tangent is positive in the 1st quadrant so that part of the graph hugs up the asymptotes. From -pi/2 to 0, cotangent is negative in the 4th quadrant so that part of the graph hugs down the asymptote. After connecting the two, we see that cotangent graph goes uphill.
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