Question

Find the value of sin [ 2π + π/3 ] ?​

Answer 1

$\sin(2\pi + \frac{\pi}{3} )$

$\sin(a + b) = \sin(a) \cos(b) + \cos(a) \sin(b)$

therefore

$= \sin(2\pi) \cos( \frac{\pi}{3} ) + \cos(2\pi) \sin( \frac{\pi}{3} ) \\ = 0 \times \frac{1}{2} + ( 1) \times \frac{ \sqrt{3} }{2} \\ = 0 + \frac{ \sqrt{3} }{2} \\ = \frac{ \sqrt{3} }{2}$

Answer 2

Answer:

√3/2

Explanation:

sin[2π + π/3]

=sin[2(180) + 180/3]

=sin[360+60]

from identity sin(A+B)=sinAcosB+cosAsinB

sin[2π + 10/3]= sin360cos60 + cos360sin60

since sin360=0 therefore sin360cos60=0

and cos360=1,sin60=√3/2

therefore sin[2π +10/3]=0+(1×√3/2)

=√3/2