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.) cscφ =

Explanation:

Step1: Find the hypotenuse

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

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

\(\csc\phi=\frac{\text{hypotenuse}}{\text{opposite}}\)
The opposite side to \(\phi\) is \(13\), and the hypotenuse is \(\sqrt{745}\)
\(\csc\phi=\frac{\sqrt{745}}{13}\)

Answer:

\(\frac{\sqrt{745}}{13}\)