## Calculus with Applications (10th Edition)

$\sin \theta=\frac{-24}{25}$ $\cos \theta=\frac{7}{25}$ $\tan \theta=\frac{-24}{7}$ $\csc \theta=\frac{-25}{24}$ $\sec \theta=\frac{25}{7}$ $\cot \theta=\frac{-7}{24}$
We are given $x=7,y=-24$ $x, y, z$ form a right-angled triangle so to find z we can apply the formula: $x^2+y^2=r^2$ $\rightarrow r=\sqrt 7^2+(-24)^2=25$ With $x=7, y=-24, z=25$, thetrigonometric functions are $\sin \theta=\frac{y}{r}=\frac{-24}{25}$ $\cos \theta=\frac{x}{r}=\frac{7}{25}$ $\tan \theta=\frac{y}{x}=\frac{-24}{7}$ $\csc \theta=\frac{1}{\sin \theta}=\frac{-25}{24}$ $\sec \theta=\frac{1}{\cos \theta}=\frac{25}{7}$ $\cot \theta=\frac{x}{y}=\frac{-7}{24}$