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

The principal value gives

Treating

is equivalent to

which is an equation with multiple solutions.

In our case,

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

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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