Question

Упростить выражение $5-sin(2\pi *10^3t)+2cos(2\pi *2*10^3t+\frac{\pi }{3} )$

Answer 1

5-sin(2$\pi$*$10^{3}$t)+2cos(2$\pi$*2*$10^{3}$t+$\frac{\pi }{3}$)

5-sin(2$\pi$*1000t)+2cos(4$\pi$*$10x^{3}$+$\frac{\pi }{3}$)

5-sin(2000$\pi$t)+2(cos(4$\pi$*$10^{3}$t)cos($\frac{\pi }{3}sin(\frac{\pi }{3} ))$

5-sin(2000$\pi$t)+2(cos(4$\pi$*$10^{3}$t)*$\frac{1}{2}$-sin(4$\pi$*$10^{3}$t)*$\frac{\sqrt{3} }{2}$)

$5-sin(2000\pi t)+2(\frac{cos(4\pi *10^{3}t }{2} -\frac{\sqrt{3}sin(4\pi *10^{3}t) }{2} )$

$5-sin(2000\pi t)+2*\frac{cos(4\pi *10^3t)-\sqrt{3}sin(4\pi *10^3t) }{2}$

5-sin(2000$\pi t$)$+cos(4\pi *10^3t)-\sqrt{3} (4\pi *10^3t)$

$5-sin(200\pi t)+cos(4\pi *1000t)-3sin(4\pi *1000t)$

$5-sin(2000\pi t)+cos(4000\pi t)-\sqrt{3} sin(4\pi *1000t)$