# In the interval 90^@<=A<=360^@, what's the smallest value of A for which cotA is undefined?

${180}^{o}$

#### Explanation:

$\cot A = \cos \frac{A}{\sin} A$

And so $\cot A$ will be undefined when $\sin A = 0$

We're asked for the smallest value of A within the interval:

${90}^{o} \le A \le {360}^{o}$

The sine ratio is 0 at ${0}^{o} \pm n {180}^{o}$ where n is a natural number. And so the smallest value of A within our allowable range that will make $\sin A = 0$ and therefore make $\cot A$ undefined is ${180}^{o}$