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# 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) $$\frac{-1}{2}$$, $$\frac{\sqrt{-3}}{2}$$, $$\frac{\sqrt{3}}{3}$$

### 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 $$\frac{3}{3}$$ = $$\frac{3}{3}$$
∴ = $$\frac{-1}{2}$$, $$\frac{\sqrt{-3}}{2}$$, $$\frac{\sqrt{3}}{3}$$

## 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 $$\frac{3}{3}$$ = $$\frac{3}{3}$$
∴ = $$\frac{-1}{2}$$, $$\frac{\sqrt{-3}}{2}$$, $$\frac{\sqrt{3}}{3}$$