Question

Вычислите: sin(-9π)+2cos(25π)/3-сtg(11π)/4

Answer 1

$sin(-9\pi)+2cos\frac{25\pi}{3}-ctg\frac{11\pi}{4}=$

$-sin(9\pi)+2cos(8\pi+\frac{\pi}{3})-ctg(2\pi+\frac{3\pi}{4})=$

$-sin(8\pi+\pi)+2cos\frac{\pi}{3}-ctg\frac{3\pi}{4}=$

$-sin\pi+2\cdot\frac{1}{2}-ctg(\pi-\frac{\pi}{4})=$

$0+2\cdot\frac{1}{2}-ctg(\pi-\frac{\pi}{4})=$

$1+ctg\frac{\pi}{4}=$

$1+1=2$