Answer:
There are two options: b) [tex]\frac{\sqrt{15}}{4}[/tex], c) [tex]\sqrt{15}[/tex].
Step-by-step explanation:
By Trigonometry, we know that function tangent is equal to the following identity in terms of functions sine and cosine:
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex] (1)
If we know that [tex]\tan \theta > 0[/tex] and [tex]\sin \theta = \frac{1}{4}[/tex], then [tex]\cos \theta > 0[/tex]. Hence, we have two possibilities: b) [tex]\frac{\sqrt{15}}{4}[/tex], c) [tex]\sqrt{15}[/tex].
