Wyznacz liczbę a

[asiula0321]

Wyznacz liczbę \(\displaystyle{ a=log _{16}sin \frac{3}{4} \pi+16 ^{cos\frac{2\pi}{3}}}\)

[kajus]

\(\displaystyle{ a=log _{16}sin \frac{3}{4} \pi+16 ^{cos\frac{2\pi}{3}}=\\ \\
log _{16}sin (\pi-\frac{1}{4}\pi) +16^{cos(\pi-\frac{1}{3}\pi)}=\\ \\
log _{16}sin \frac{\pi}{4} +16^{-cos\frac{\pi}{3}}=\\ \\
log _{16} \frac{\sqrt2}{2} +16^{-\frac{1}{2}}= \\ \\
-\frac{1}{8}+\frac{1}{4}=\frac{3}{8}\\}\)