Answer :
The exact value is -[tex]\sqrt{3}[/tex]/2
What is trigonometry quadrant ?
Quadrants & Quadrantal Angles
Angles between 0∘ and 90∘ are in the first quadrant. Angles between 90∘ and 180∘ are in the second quadrant. Angles between 180∘ and 270∘ are in the third quadrant. Angles between 270∘ and 360∘ are in the fourth quadrant.
Solution,
Remove full rotations of 2π until the angle is between 0 and 2π.
sin (2π + 4π/3)
sin(4π/3)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.
sin(π + π/3)
= - sin(π/3) (The exact value of sin(π/3)=[tex]\sqrt{3}[/tex]/2)
= -[tex]\sqrt{3}[/tex]/2
or
= - 0.86602540
hence, the exact value is -[tex]\sqrt{3}[/tex]/2
To learn more about trigonometry quadrant from here
https://brainly.in/question/1525791
#SPJ2