The sine, cosine and tangent of 210° 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 \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)
jamb 1987mathematics

The correct answer is D. \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)

210° = 180° - 210° = - 30°

From ratio of sides, sin -30° = -\(\frac{1}{2}\)

Cos 210° = 180° - 210° = -30°

= cos -30° = \(\frac{-3}{2}\)

But tan 30° = \(\frac{1}{\sqrt{3}}\), rationalizing this

= \(\frac{1}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\) = \(\frac{\sqrt{3}}{3}\)

∴ = \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)

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