Question

Resolva as expressões:

a) cos1080º . tg (-405º)
_________________
______sen930º


_____14π___( __10π _____29π_)
b) sen_____ . (tg___ - cos _____)
_____3_____(___3 ______6___)

Answer 1

a)

$A = \frac{\cos(1080\textdegree)\tan(-405\textdegree)}{\sin(930\textdegree)} \\A=\frac{\cos(0\textdegree) \tan(-45\textdegree)}{\sin(210\textdegree)} \\A=\frac{\cos(0\textdegree) \tan(-45\textdegree)}{-\sin(30\textdegree)}\\A=\frac{1 \times (-1)}{-\frac{1}{2}} \\A=-1\times-\frac{2}{1}\\ A=2$

b)

$B = \sin\frac{14\pi}{3}(\tan\frac{10\pi}{3}-\cos\frac{29\pi}{6})\\B = \sin120\textdegree(\tan240\textdegree-\cos150\textdegree)\\B = \sin60\textdegree(\tan60\textdegree+\cos30\textdegree)\\B = \frac{\sqrt{3}}{2}(\sqrt{3}+\frac{\sqrt{3}}{2})\\B = \frac{\sqrt{3}}{2}\times\sqrt{3}+\frac{\sqrt{3}}{2}\times\frac{\sqrt{3}}{2}\\B = \frac{3}{2}+\frac{3}{4}\\B = \frac{6}{4}+\frac{3}{4}\\B = \frac{9}{4}$