Answer:
Step-by-step explanation:
Recall that on the unit circle, each point is represented as [tex](\cos(\theta), \sin(\theta))[/tex] where [tex]0\leq \theta \leq 2\pi[/tex]. In this case, we are asked to take a loot at the interval [tex] 0 \leq \theta \leq \pi[/tex].
We will use the definition of tangent to solve the problem. REcall that
[tex]\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex]
So, in this case, tangent is undefined whenever the denominator is zero. That is, when [tex]\cos(\theta)=0[/tex]. Checking the unit circle with the interval [tex] 0 \leq \theta \leq \pi[/tex], 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 [tex]\cos(\theta)=0[/tex].
. This happens only at the point (0,1), which is associated with the value of [tex]\theta = \frac{\pi}{2}[/tex]
