Home » Past Questions » Mathematics » The sine, cosine and tangent of 210o are respectively

The sine, cosine and tangent of 210o are respectively


Question

The sine, cosine and tangent of 210o are respectively

Options

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

The correct answer is 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 = \(\frac{1}{3}\), rationalizing this
= \(\frac{1}{3}\) x \(\frac{3}{3}\) = \(\frac{3}{3}\)
∴ = \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)

More Past Questions:


Dicussion (1)

  • 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 = \(\frac{1}{3}\), rationalizing this
    = \(\frac{1}{3}\) x \(\frac{3}{3}\) = \(\frac{3}{3}\)
    ∴ = \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)

    Reply
    Like