Question

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

Answer 1

Answer:

Step-by-step explanation:

Recall that on the unit circle, each point is represented as $(\cos(\theta), \sin(\theta))$ where $0\leq \theta \leq 2\pi$. In this case, we are asked to take a loot at the interval $0 \leq \theta \leq \pi$.

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

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

So, in this case, tangent is undefined whenever the denominator is zero. That is, when $\cos(\theta)=0$. Checking the unit circle with the interval $0 \leq \theta \leq \pi$, 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 $\cos(\theta)=0$.

. This happens only at the point (0,1), which is associated with the value of $\theta = \frac{\pi}{2}$