Question

find the six trigonometric function values of the specified angle.
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)
\\( \csc \phi= \\)
(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 \(a^{2}+b^{2}=c^{2}\), where \(a = 10\), \(b=24\).
\(c=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26\)

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

\(\csc\phi=\frac{\text{hypotenuse}}{\text{opposite}}\)
The opposite side to \(\phi\) is \(24\), and the hypotenuse \(c = 26\)
\(\csc\phi=\frac{26}{24}=\frac{13}{12}\)

Answer:

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