Question

SOCORROOOO
calcule o valor de:
Y=7.cos19π/3+2.cosπ/2-3.cos9π/4
​

Answer 1

$\displaystyle \text Y = 7\text{cos}(\frac{19\pi}{3})+2\text{cos}(\frac{\pi}{2})-3\text{cos}(\frac{9\pi}{4})$

temos :

$\displaystyle \text{cos} (\frac{19\pi}{3}) \to \text {cos}(6\pi + \frac{\pi}{3}) = \text{cos}(\frac{\pi}{3}) = \frac{1}{2} \\\\\\ \text{cos}(\frac{\pi}{2}) = 0 \\\\\\ \text{cos}(\frac{9\pi}{4})\to \text{cos}(2\pi + \frac{\pi}{4}) = \text{cos}(\frac{\pi}{4}) = \frac{\sqrt 2}{2}$

Substituindo na equação original :

$\displaystyle \text Y = 7\text{cos}(\frac{19\pi}{3})+2\text{cos}(\frac{\pi}{2})-3\text{cos}(\frac{9\pi}{4}) \\\\ \text Y = \frac{7}{2}+2.0 -\frac{3\sqrt2}{2} \\\\\\ \huge\boxed{\text Y = \frac{7-3\sqrt{2}}{2}\ }\checkmark$