Answer:
[tex]\cos \theta = \frac{\sqrt{15}}{4}}[/tex]
Step-by-step explanation:
Recall that [tex]\sin(-\theta)=-\sin(\theta)[/tex]. Therefore, [tex]\sin\theta=-(-\frac{1}{4})=\frac{1}{4}[/tex]
In any right triangle:
- The sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle (o/h)
- The cosine of an angle is equal to its adjacent side divided by the hypotenuse of the triangle (a/h)
- The tangent of an angle is equal to its opposite side divided by its adjacent side (o/a)
From [tex]\sin \theta=\frac{1}{4}[/tex] and [tex]\tan \theta = \frac{\sqrt{15}}{15}[/tex], we know:
- [tex]\theta[/tex]'s opposite side is 1
- [tex]\theta[/tex]'s adjacent side is [tex]\sqrt{15}[/tex]
- The hypotenuse of the triangle is 4
Therefore, the desired answer is [tex]\boxed{\cos \theta = \frac{\sqrt{15}}{4}}}[/tex].
