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

Explanation:

Step1: Find the hypotenuse \( c \)

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: Calculate \( \cos\phi \)

The formula for cosine in a right - triangle is \( \cos\phi=\frac{\text{adjacent}}{\text{hypotenuse}} \).
The adjacent side to angle \( \phi \) is \( 13 \), and the hypotenuse \( c=\sqrt{13^{2}+24^{2}}=\sqrt{745} \). So \( \cos\phi=\frac{13}{\sqrt{745}}=\frac{13\sqrt{745}}{745}\)

Answer:

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