Question

The sine of an angle is `4/5`. What is the tangent of the angle?

Answer 1

The tangent of the angle could be `4/3` or `-4/3`.

Explanation:

There are two possibilities, depending on what quadrant the angle A is in.

We have `sin(A) = 4/5` so we could make a triangle with `opp = 4` and `hyp = 5`.

Solving `4^2 + x^2 = 5^2` we get `x = adj = +-3`.

This means that `tan(A) = (opp)/(adj) = +-4/3`.

\\ dansmath strikes again! //