Question

what is the trigonometric ratio for \\( \cos n \\)?
enter your answer as a fraction in simplest form in
the boxes.

Explanation:

Step1: Recall the cosine ratio formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle N\), the adjacent side to \(\angle N\) is \(MN\) and the hypotenuse is \(LN\).

Step2: Substitute the values

We know that \(MN = 36\) and \(LN=39\). So, \(\cos N=\frac{MN}{LN}=\frac{36}{39}\).

Step3: Simplify the fraction

Find the greatest common divisor (GCD) of 36 and 39. The factors of 36 are \(1,2,3,4,6,9, 12,18,36\) and the factors of 39 are \(1,3,13,39\). The GCD of 36 and 39 is 3. Divide both the numerator and the denominator by 3: \(\frac{36\div3}{39\div3}=\frac{12}{13}\).

Answer:

\(\frac{12}{13}\)