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

cos(5pi/6)
cos(5pi/3)
sin(pi/3)
sin(7pi/6)

(A)

Step-by-step explanation:

The given trigonometric ratio is :

On solving this, we get

=

=

=

=

(A) The given trigonometric ratio is :

=

=

=

=

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

(B) The given trigonometric ratio is :

=

=

=

=

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

(C) The given trigonometric ratio is :

=

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

(D) The given trigonometric ratio is :

=

=

=

=

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

the answer is b.)

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