Answer:
opposite side -√3
--------------------- = -------- = sin -2π/3
hypotenuse 2
Step-by-step explanation:
Note that +π/3 radians corresponds to +60°, and so +2π/3 radians corresponds to +120°. Similarly, -π/3 radians corresponds to -60°, and so -2π/3 radians corresponds to -120°.
-2π/3 radians is in Quadrant III. The "opposide" (the side opposite the angle) has length √3 when the radius of the circle is 2; because this angle is in Q III, we give it the - sign: -√3.
Thus, the sine of -2π/3 is:
opposite side -√3
--------------------- = -------- = sin -2π/3
hypotenuse 2
