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Answer 1

The exact value of sin 4π/3 is -√3/2 and tan 4π/3 is √3.

sin 4π/3 can be written as sin(4x180)/3 = sin 240°

240° lies in third quadrant where only tan and cot are positive.

So, sin 240° will be a negative value.

sin 240° = sin(180+60)° = -sin 60° = -√3/2

tan 4π/3 can be written as tan(4x180)/3 = tan 240°

240° lies in third quadrant where only tan and cot are positive.

So, tan 240° will be a positive value.

tan 240° = tan(180+60)° = tan 60° = √3

Thus, the value of sin 4π/3 is -√3/2 and tan 4π/3 is √3.

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