On the unit circle, where 0 less-than pi, when is tangent theta undefined? Theta = pi and Theta = 2 pi

sine theta = cosine theta

Pi = StartFraction pi Over 2 EndFraction and Pi = StartFraction 3 pi Over 2 EndFraction

sin theta = StartFraction 1 Over cosine theta EndFraction

Step-by-step explanation:

Recall that on the unit circle, each point is represented as where . In this case, we are asked to take a loot at the interval .

We will use the definition of tangent to solve the problem. REcall that

So, in this case, tangent is undefined whenever the denominator is zero. That is, when . Checking the unit circle with the interval , this restriction corresponds to the upper half of the unit circle. In this case, the x component of each point is cosine. We are interested at the points where .

. This happens only at the point (0,1), which is associated with the value of