Question

what is the cosine of \\( \theta \\)?
\\( \cos \theta = \frac { ? } { \square } \\)

Explanation:

Step1: Recall the unit - circle definition of cosine

On the unit circle \(x^{2}+y^{2}=1\), for a point \((x,y)\) on the unit circle corresponding to an angle \(\theta\), \(\cos\theta=x\).

Step2: Identify the \(x\) - coordinate of the given point

The given point is \((\frac{1}{4},\frac{\sqrt{15}}{4})\). The \(x\) - coordinate of this point is \(\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)