Answer
$\sin \theta=\frac{-24}{25}$
$\cos \theta=\frac{7}{25}$
$\tan \theta=\frac{-24}{7}$
$\csc \theta=\frac{-25}{24}$
$\sec \theta=\frac{25}{7}$
$\cot \theta=\frac{-7}{24}$
Work Step by Step
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
$\sin \theta=\frac{y}{r}=\frac{-24}{25}$
$\cos \theta=\frac{x}{r}=\frac{7}{25}$
$\tan \theta=\frac{y}{x}=\frac{-24}{7}$
$\csc \theta=\frac{1}{\sin \theta}=\frac{-25}{24}$
$\sec \theta=\frac{1}{\cos \theta}=\frac{25}{7}$
$\cot \theta=\frac{x}{y}=\frac{-7}{24}$
