4sin(theta) = 5cos(theta) - write in the form tan(theta) =

Question:

4sin(theta) = 5cos(theta) - write in the form tan(theta) =

I would have thought according to the identity, tan(x) = sin (x) / cos (x)

that it would be tan(x) = 4 / 5

but the solutions in my text book have tan(x) = 5/4

\(\begin{array}{|rcll|} \hline 4\cdot \sin(\theta) &=& 5\cdot \cos(\theta) \quad & | \quad : \cos(\theta) \\ 4\cdot \frac{ \sin(\theta) } {\cos(\theta)} &=& 5 \quad & | \quad : 4 \\ \frac{ \sin(\theta) } {\cos(\theta)} &=& \frac{5}{4} \quad & | \quad \frac{ \sin(\theta) } {\cos(\theta)} = \tan(\theta) \\ \tan(\theta) &=& \frac{5}{4} \\ \hline \end{array}\)