Answer:
(A)
Step-by-step explanation:
The given trigonometric ratio is :
[tex]sin\frac{4{\pi}}{3}[/tex]
On solving this, we get
[tex]sin\frac{4{\pi}}{3}[/tex]
=[tex]sin240^{{\circ}}[/tex]
=[tex]sin(180+60)[/tex]
=[tex]-sin60^{{\circ}}[/tex]
=[tex]-\frac{\sqrt{3}}{2}[/tex]
(A) The given trigonometric ratio is :
[tex]cos\frac{5{\pi}}{6}[/tex]
=[tex]cos150^{{\circ}}[/tex]
=[tex]cos(180-30)[/tex]
=[tex]-cos30^{{\circ}}[/tex]
=[tex]-\frac{\sqrt{3}}{2}[/tex]
Which is equivalent to the given trigonometric ratio, thus (A) is correct.
(B) The given trigonometric ratio is :
[tex]cos\frac{5{\pi}}{3}[/tex]
=[tex]cos300^{{\circ}}[/tex]
=[tex]cos(360-60)[/tex]
=[tex]-cos60^{{\circ}}[/tex]
=[tex]-\frac{1}{2}[/tex]
which is not equivalent to the given trigonometric ratio, thus(B) is incorrect.
(C) The given trigonometric ratio is :
[tex]sin\frac{{\pi}}{3}[/tex]
=[tex]\frac{\sqrt{3}}{2}[/tex]
which is not equivalent to the given trigonometric ratio, thus(C) is incorrect.
(D) The given trigonometric ratio is :
[tex]sin\frac{7{\pi}}{6}[/tex]
=[tex]sin210^{{\circ}}[/tex]
=[tex]sin(180+30)[/tex]
=[tex]-sin30^{{\circ}}[/tex]
=[tex]-\frac{1}{2}[/tex]
which is not equivalent to the given trigonometric ratio, thus(D) is incorrect.
