## Algebra 2 (1st Edition)

For $\theta=90^{\circ}$, $\cos \theta=\cos 90^{\circ}=0$ Thus, the function tangent is undefined. AND For $\theta=90^{\circ}$, $\sin \theta=\sin 90^{\circ}=1 \neq 0$ Thus, the function cotangent is defined.
Since, $\tan \theta=\dfrac{Opposite}{Adjacent}=\dfrac{y}{x}$ and $\tan \theta=\dfrac{\sin \theta }{\cos \theta}$ when $\cos \theta=0$, then the tangent function will be undefined. For $\theta=90^{\circ}$, $\cos \theta=\cos 90^{\circ}=0$ Thus, the function tangent is undefined. Also, $\cot \theta=\dfrac{1}{\dfrac{\sin \theta }{\cos \theta}}$ Thus, $\cot \theta=\dfrac{\cos \theta }{\sin \theta}$ For $\theta=90^{\circ}$, $\sin \theta=\sin 90^{\circ}=1 \neq 0$ Thus, the function cotangent is defined.