Question

1. \\( \tan ( 630 ^ { \circ } ) \\)

a) undefined b) 0 c) -1 d) 1

Explanation:

Step1: Reduce the angle

We know that the tangent function has a period of \(180^{\circ}\) (or \(\pi\) radians). So, \(630^{\circ}= 360^{\circ}+ 270^{\circ}\). Then \(\tan(630^{\circ})=\tan(360^{\circ} + 270^{\circ})\).
Since \(\tan(x + 360^{\circ}n)=\tan(x)\) for \(n\in\mathbb{Z}\), we have \(\tan(630^{\circ})=\tan(270^{\circ})\).

Step2: Use the unit - circle and tangent definition

The tangent function is defined as \(\tan\theta=\frac{\sin\theta}{\cos\theta}\). For \(\theta = 270^{\circ}\), \(\sin(270^{\circ})=- 1\) and \(\cos(270^{\circ}) = 0\).

Answer:

A. Undefined