# Chapter 13, Trigonometric Ratios and Functions - 13.3 Evaluate Trigonometric Functions of Any Angle - 13.3 Exercises - Skill Practice - Page 871: 33

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.

#### Work Step by Step

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.

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