Question

find the six trigonometric function values of the specified angle.

cosφ = \frac{13\sqrt{745}}{745}
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

tanφ = \square
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Find the hypotenuse

Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 13\) and \(b=24\).
\(c=\sqrt{13^{2}+24^{2}}=\sqrt{169 + 576}=\sqrt{745}\)

Step2: Recall the definition of \(\tan\phi\)

\(\tan\phi=\frac{\text{opposite}}{\text{adjacent}}\)
In a right - triangle, for angle \(\phi\), the opposite side is \(24\) and the adjacent side is \(13\)

Answer:

\(\frac{24}{13}\)