Question

Вычислите функции: а) sin(-13п/4); б)tg(-19п/6); в) cos(13п/6); г) ctg(7п/4)

Answer 1

$a)\;\sin\left(-\frac{13\pi}4\right)=-\sin\frac{13\pi}4=-\sin\left(2\pi+\frac{5\pi}4\right)=-\sin\frac{5\pi}4=\\=-\left(-\frac1{\sqrt2}\right)=\frac1{\sqrt2}\\\\b)\;tg\left(-\frac{19\pi}6\right)=-tg\frac{19\pi}6=-tg\left(3\pi+\frac\pi6\right)=-tg\frac\pi6=-\frac1{\sqrt3}\\\\c)\;\cos\frac{13\pi}6=\cos\left(2\pi+\frac\pi6\right)=\cos\frac\pi6=\frac{\sqrt3}2\\\\d)\;ctg\frac{7\pi}4=ctg\left(\pi+\frac{3\pi}4\right)=ctg\frac{3\pi}4=-1$