Question

$\sin( \frac{2x}{3} ) + \cos( \frac{3x}{2} )$
calculati

Answer 1

   
[tex]\displaystyle\\ f(x)= \sin\left(\frac{2x}{3}\right)+\cos\left( \frac{3x}{2} \right) \\\\\\ f\left( \frac{\pi}{2} \right)= \sin\left( \frac{2\cdot \dfrac{\pi}{2}}{3} \right) + \cos\left( \frac{3\cdot \dfrac{\pi}{2}}{2} \right)=\\\\\\ = \sin\left( \frac{\pi }{3} \right) + \cos\left( \frac{3\pi}{4} \right)=\\\\\\ = \sin 60^o + \cos 135^o =\\\\ = \frac{ \sqrt{3} }{2} + \cos(180 - 45)=\\\\ = \frac{ \sqrt{3} }{2} - \cos 45=\\\\ = \frac{ \sqrt{3} }{2}-\frac{\sqrt{2}}{2}=\boxed{\frac{\sqrt{3}-\sqrt{2}}{2}} [/tex]

Raspuns corect:  a)