obliczyć korzystając ze wzoru

[mateusz.ex]

oblicz \(\displaystyle{ sin 22.5}\)(stopni)
skorzystaj ze wzoru podanego niżej.

\(\displaystyle{ sin( - )=sin cos -cos sin }\)

[wb]

\(\displaystyle{ sin22,5^0=sin(45^0-22,5^0)=sin45^0cos22,5^0-cos45^0sin22,5^0= \\= \frac{\sqrt2}{2}(cos22,5^0-sin22,5^0) \\sin22,5^0=\frac{\sqrt2}{2}(cos22,5^0-sin22,5^0) \ \ \ /()^2 \\ sin^222,5^0= \frac{1}{2}(cos^222,5^0-2cos22,5^0sin22,5^0+sin^222,5^0) \\ 2sin^222,5^0= 1-sin45^0\\ 2sin^222,5^0=1- \frac{\sqrt2}{2} \\ sin^222,5^0= \frac{1}{2}- \frac{\sqrt2}{4} \\ sin22,5^0=\sqrt{ \frac{1}{2}- \frac{\sqrt2}{4}}}\)