sin 4𝜋/3 𝑜𝑟 (8𝜋/6)
−√3/2
Both 4π/3 and 8π/6 represent the same angle in radians, which is 240 degrees or 4/3 of a full rotation around a circle.
We know that sin(240 degrees) or sin(4π/3) is negative, because the sine function is negative in the third quadrant of the unit circle, where the angle 240 degrees lies. The sine function represents the vertical component of a point on the circle and the horizontal component represents the cosine function, as shown in the following diagram:
“`
|
+ y |
QII | QI
(-x, +y) ——+——> (+x, +y)
|\
| \
| \ + x
| \
|____\____
QIII QIV
(+x, -y) (-x, -y)
“`
Therefore, we can use the sine function to find the answer:
“`
sin(4π/3) = sin(8π/6) = -√3/2
“`
Thus, the value of sin(4π/3) or sin(8π/6) is -√3/2.
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