# How do you evaluate #tan(arcsin( 2/3)) #?

##### 1 Answer

The principal value gives

Treating

#### Explanation:

This question has a different answer depending on whether we interpret

Let's answer first considering

is equivalent to

which is an equation with multiple solutions.

Then there are two possible values for

In our case,

That's also apparent if we treat the right triangle in question as having opposite side

So we get

In the case when we're talking about the principal value of the inverse sine, a positive sine ends us in the first quadrant, so a positive tangent as well. We'll write this