3sinx-4cosx-k =0
利用辅助角公式,整磨腔理
5sin(x+s) =k,
s =arctan(-4/3)
sin(x+s) =k/5
sin(x+s)有意大如义
-1≤k/5≤1
解得, -5≤滚游启k≤5
3sinx-4cosx=k
5sin(x-a)=k
tana=4/3
-5≤k≤5
方程两边同除以5,得3/锋坦让5*sinx-4/5*cosx=k/5;
令:cosy=3/5,则:银局siny=4/5,
有:sin(x-y)=k/5
由-1<=sin(x-y)<=1得信梁,-1<=(k/5)<=1
得,-5<=k<=5
k=3sinx-4cosx
k=5sin(x+t) tan(t)=4/3
所以-5<=k<=5