Question

Which of the following trigonometric ratios is equivalent to sin 4pi / 3?

Answer 1

Answer:

(A)

Step-by-step explanation:

The given trigonometric ratio is :

$sin\frac{4{\pi}}{3}$

On solving this, we get

$sin\frac{4{\pi}}{3}$

=$sin240^{{\circ}}$

=$sin(180+60)$

=$-sin60^{{\circ}}$

=$-\frac{\sqrt{3}}{2}$

(A) The given trigonometric ratio is :

$cos\frac{5{\pi}}{6}$

=$cos150^{{\circ}}$

=$cos(180-30)$

=$-cos30^{{\circ}}$

=$-\frac{\sqrt{3}}{2}$

Which is equivalent to the given trigonometric ratio, thus (A) is correct.

(B) The given trigonometric ratio is :

$cos\frac{5{\pi}}{3}$

=$cos300^{{\circ}}$

=$cos(360-60)$

=$-cos60^{{\circ}}$

=$-\frac{1}{2}$

which is not equivalent to the given trigonometric ratio, thus(B) is incorrect.

(C) The given trigonometric ratio is :

$sin\frac{{\pi}}{3}$

=$\frac{\sqrt{3}}{2}$

which is not equivalent to the given trigonometric ratio, thus(C) is incorrect.

(D) The given trigonometric ratio is :

$sin\frac{7{\pi}}{6}$

=$sin210^{{\circ}}$

=$sin(180+30)$

=$-sin30^{{\circ}}$

=$-\frac{1}{2}$

which is not equivalent to the given trigonometric ratio, thus(D) is incorrect.