Question

利用图形求sin15°如图,欲求sin15°的值,可先画Rt△ABC,使∠C=90°,∠BAC=30°,再延长CA到D,

Answer 1

不妨设BC=1,则AC=√3,AB=AD=2

BD^2=BC^2+CD^2=1+(2+√3)^2=8+4√3=2(√3+1)^2

BD=√2(√3+1)=√6+√2

sin15°=1/(√6+√2)=(√6-√2)/4