6) \\( \\tan ( 630 ^ { \\circ } ) \\)\na) undefined b) 0 c) -1 d) 1
6) \\( \\tan ( 630 ^ { \\circ } ) \\)\na) undefined b) 0 c) -1 d) 1
Answer
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