Construction of Tangent graph
The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. The construction was simple as we go off the construction of the Sine and Cosine graphs. We know that tan=sin/cos. Using that information, we plot a point T = (t,y(Q)/x(Q)). The Q represents the point on the unit circle and the y-coordinates. The tangent will be zero when the numerator (the sine) is 0. This happens at 0, π, 2π, 3π, etc, and at –π, –2π, –3π, etc. The tangent will be undefined wherever its denominator (the cosine) is zero. A zero in the denominator means you'll have a vertical asymptote. So the tangent will have vertical asymptotes wherever the cosine is zero: at –π/2, π/2, and 3π/2.