Răspuns:
[tex]sin\dfrac{23\pi }{4} =sin\dfrac{24\pi -\pi }{4} =sin(\dfrac{24\pi }{4}-\dfrac{\pi }{4})=sin(2\pi*3-\dfrac{\pi }{4})=sin(-\dfrac{\pi }{4})=-sin\dfrac{\pi }{4}=-\dfrac{\sqrt{2} }{2}.~~Deci~sin^{2} \dfrac{23\pi }{4} =(-\dfrac{\sqrt{2} }{2})^{2}=\dfrac{2}{4}=\dfrac{1}{2}.\\[/tex]
[tex]tg\dfrac{37\pi }{4}= tg\dfrac{36\pi+\pi }{4}=tg(9\pi +\dfrac{\pi }{4} )=tg\dfrac{\pi }{4}=1.\\Deci~tg^{2}\dfrac{37\pi }{4}=1;~~~ctg(-\dfrac{\pi }{4})=-ctg(\dfrac{\pi }{4})=-1[/tex]
Atunci F=2·(1/2)+1·(-1)=1-1=0.
Explicație pas cu pas:
