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Setler79 [48]
3 years ago
12

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

Mathematics
1 answer:
topjm [15]3 years ago
4 0

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}

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