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

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\). Here \(a = 24\), \(b = 10\) (assuming the other side is \(10\) as \(13\) might be a mis - read, if it's a right - triangle with legs \(24\) and \(10\)), then \(c=\sqrt{24^{2}+10^{2}}=\sqrt{576 + 100}=\sqrt{676}=26\).

Step2: Calculate \(\cos\phi\)

The cosine formula for a right - triangle is \(\cos\phi=\frac{\text{adjacent}}{\text{hypotenuse}}\). The adjacent side to \(\phi\) is \(24\) and the hypotenuse \(c = 26\). So \(\cos\phi=\frac{24}{26}=\frac{12}{13}\).

Answer:

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