Question

tình hinh$sin(\frac{2x}{3} -\frac{\pi }{3} )=0$

Answer 1

Answer:

$\rm\dfrac{\pi}{2}$

Step-by-step explanation:

We are here given a trigonometric equation and we need to find the value of x. The given equation is ,

$\rm\implies sin\bigg( \dfrac{2x}{3}-\dfrac{\pi}{3}\bigg)= 0$

Now as we know that ,

$\rm\implies \red{ sin 0^o = 0 }$

So that ,

$\rm\implies sin\bigg( \dfrac{2x}{3}-\dfrac{\pi}{3}\bigg)= sin(0^o)$

On comparing , we have ;

$\rm\implies \dfrac{2x}{3}-\dfrac{\pi}{3}=0$

Adding π/3 to both sides ,

$\rm\implies \dfrac{2x}{3}=\dfrac{\pi}{3}$

Cancel 3 in the denominator ,

$\rm\implies 2x = \pi$

Finally divide both sides by 2 ,

$\rm\implies \boxed{\pink{\frak{ x =\dfrac{\pi}{2}=90^{\circ}}}}$