4sinA+6cosA=?

题目

4sinA+6cosA=?

答案

4sina+6cosa
=√52[(4/√52)sina+(6/√52)cosa]
设cosb=4/√52,且b是锐角
则(sinb)^2=1-(cosb)^2=36/52
sinb=6/√52
tanb=sinb/cosb=4/6
b=arctan(4/6)
所以4sina+6cosa
=√52(sinacosb+cosasinb)
=√52sin(a+b)
=√52*sin[a+arctan(4/6)]
总之asinx+bcosx=√(a^2+b^2)*sin[x+arctan(b/a)]