Question

Find the angle with a tangent ratio of 0.4877.

Answer 1

OK, that is positive, so what quadrants have positive tangents?

Answer 2

Once you know that, then:

\(\tan\theta =0.4877\implies\)

\(\arctan(\tan\theta) =\arctan(0.4877)\implies\)

\(\theta =\arctan(0.4877)\)

After that, you put the two facts together to find the possible angles that answer your question.