csc[arccos(17361745)],如何計算這道題
- 2022-08-29
csc[arccos(1736/1745)]
設x=arccos(1736/1745)
則cosx=1736/1745
那麼,csc[arccos(1736/1745)]
=cscx
=1/sinx
=1/√(1-cos²x)
=1/√[1-(1736/1745)²]
=1/√(31329/1745²)
=1/√( 177 ²/1745²)
=1/( 177 /1745)
=1745/177
所以csc[arccos(1736/1745)]=1745/177
設 x=arccos(1736/1745)
∴ cosx=1736/1745 0 ∴ sinx=√(1-cos²x)=177/1745 原式=cscx=1/sinx=1745/177