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: Option 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})