What is the exact value of sin(-2pi/3)

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

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of