Question

evaluate sin 120 degree​

Answer 1

Answer:

The answer is $\dfrac{\sqrt 3}{2}$

Step-by-step explanation:

Using $\sin 2\theta=2\sin\theta\cos\theta$

We have

      $\sin 120^\circ=\sin(2\times 60^\circ)=2\sin60^\circ\times \cos60^\circ$

                   $=2\times \dfrac{\sqrt 3}{2}\times \dfrac{1}{2}=\dfrac{\sqrt3}{2}$

 Another method :

$\sin(120^\circ)=\sin(180^\circ-60^\circ)=\sin 60^\circ=\dfrac{\sqrt3}{2}$

Answer 2

Answer:

The answer is \dfrac{\sqrt 3}{2}

2

3

Step-by-step explanation:

Using \sin 2\theta=2\sin\theta\cos\thetasin2θ=2sinθcosθ

We have

\sin 120^\circ=\sin(2\times 60^\circ)=2\sin60^\circ\times \cos60^\circsin120

∘

=sin(2×60

∘

)=2sin60

∘

×cos60

∘

=2\times \dfrac{\sqrt 3}{2}\times \dfrac{1}{2}=\dfrac{\sqrt3}{2}=2×

2

3

×

2

1

=

2

3

Another method :

\sin(120^\circ)=\sin(180^\circ-60^\circ)=\sin 60^\circ=\dfrac{\sqrt3}{2}sin(120

∘

)=sin(180

∘

−60

∘

)=sin60

∘

=

2

3

hope it helps ♡

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