Unit T Big Question #3

THE THIRD BIG QUESTION:
Why is a normal tangent graph uphill, but a normal cotangent graph downhill?





The normal tangent graph is uphill for several reasons. Let's start with identities. Tangent equals sine over cosine, and when cosine equals zero, the value becomes undefined. This occurs when the degree value is 90 (pi/2) and 270 (3pi/2). So this means that at these values, there will be asymptotes. Now let's recall ASTC. In the first quadrant, tangent is positive, so the line will begin from the y-axis going upwards (because it's positive) towards the asymptote located at pi/2. The opposite happens in the next quadrant, then the pattern repeats (remember this from previous blog posts). Cotangent is equal to cosine over sine, so let's go with the same logic we used with tangent. If sine were to be 0, then it would become undefined (aka, an asymptote would be present). This occurs at zero degrees, pi, and 2pi.