Question

find the exact values of six trigonometric ratios for the mentioned angle.
(c)
\\( \angle w \\)
\\( \frac { \sin \frac { o } { n } } { } = \\)
\\( \frac { \cos \frac { a } { n } } { } = \\)
\\( \frac { \tan \frac { o } { a } } { } = \\)

Explanation:

Step1: Recall trigonometric ratio definitions

For a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\)

Step2: Identify sides relative to \(\angle W\)

For \(\angle W\), the opposite side \(= 5\), the adjacent side \(= 12\), and the hypotenuse \(= 13\)

Step3: Calculate \(\sin W\)

\(\sin W=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{13}\)

Step4: Calculate \(\cos W\)

\(\cos W=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{12}{13}\)

Step5: Calculate \(\tan W\)

\(\tan W=\frac{\text{opposite}}{\text{adjacent}}=\frac{5}{12}\)

Answer:

\(\sin W=\frac{5}{13}\), \(\cos W=\frac{12}{13}\), \(\tan W=\frac{5}{12}\)