The sine, cosine and tangent of 210o are respectively
A. \(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\), \(\frac{\sqrt{3}}{2}\) B. \(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\), \(\frac{\sqrt{3}}{3}\) C. \(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\), \(\frac{\sqrt{3}}{2}\) D. \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)
Correct Answer: D
Explanation
210o = 180o - 210o = - 30o From ratio of sides, sin -30o = -\(\frac{1}{2}\) Cos 210o = 180o - 210o = -30o = cos -30o = \(\frac{-3}{2}\) But tan 30o = \(\frac{1}{\sqrt{3}}\), rationalizing this = \(\frac{1}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\) = \(\frac{\sqrt{3}}{3}\) ∴ = \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)
