Question

sin 390 cos 420 tg 780 ctg 405

Answer 1

sin 390 cos 420 tg 780 ctg 405=?

sin390=sin(360+30)=sin30=1/2

cos420=cos(360+60)=cos60=1/2

tg780=tg(360*2+60)=tg60=sqrt{3}

ctg405=ctg(360+45)=ctg45=1

sin 390 cos 420 tg 780 ctg 405=1/2 *1/2 *sqrt{3} *1=sqrt{3}/4

Answer 2

$sin390textdegreecdot cos420textdegreecdot text{tg}780textdegreecdot text{ctg}405textdegree=\\=sin(360textdegree+30textdegree)cdot cos(360textdegree+60textdegree)cdot text{tg}(4cdot 180textdegree+60textdegree)cdot text{ctg}(2cdot 180textdegree+45textdegree)=\\=sin30textdegreecdot cos60textdegreecdot text{tg}60textdegreecdot text{ctg}45textdegree=\\=dfrac 12cdot dfrac 12cdot sqrt 3cdot 1boldsymbol{=dfrac{sqrt3}4}$

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Периодичность тригонометрических функций :

sin (360° + α) = sin α

cos (360° + α) = cos α

tg (180° + α) = tg α

ctg (180° + α) = ctg α