Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Skill Practice - Page 856: 3

$\sin \theta=\dfrac{Opposite}{Hypotenuse}=\dfrac{24}{26}$ $\cos \theta=\dfrac{Adjacent}{Hypotenuse}=\dfrac{10}{26}$ $\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{24}{10}$ $\csc \theta=\dfrac{Hypotenuse}{Opposite}=\dfrac{26}{24}$ $\sec \theta=\dfrac{Hypotenuse}{Adjacent}=\dfrac{26}{10}$ $\cot \theta=\dfrac{Adjacent}{Opposite}=\dfrac{10}{24}$

Use the Pythagorean Theorem to find the Hypotenuse. $Hypotenuse=\sqrt {24^2+10^2}=\sqrt {576+100}=26$ $\sin \theta=\dfrac{Opposite}{Hypotenuse}=\dfrac{24}{26}$ $\cos \theta=\dfrac{Adjacent}{Hypotenuse}=\dfrac{10}{26}$ $\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{24}{10}$ $\csc \theta=\dfrac{Hypotenuse}{Opposite}=\dfrac{26}{24}$ $\sec \theta=\dfrac{Hypotenuse}{Adjacent}=\dfrac{26}{10}$ $\cot \theta=\dfrac{Adjacent}{Opposite}=\dfrac{10}{24}$