Evaluate the expression a. arctan ( - \sqrt{3} ) b. arctan ( - \sqrt{3} ) pls i need this asap!

Based on the link I shared above, the value of is that number that satisfies



where lies in what you might call the "principal branch". That is, is bounded below by and above by , so it's only a valid inverse of if we restrict the domain of to .

In other words, is some angle whose terminus lies in either the first or fourth quadrant (I'm assuming you're at least a little familiar with the typical unit circle diagrams used in trig). The only value of in this domain that satisfies the equation above is .

On the other hand, captures all possible values of that satisfy



First, we know that (in other words, has a period of ), so in fact as well. In general, then, we know that will be a valid solution to the equation above, where is any integer.

Earlier we found that , so in this case, for .