Question

若直线x=π/6是函数y=asinx+bcosx图像的一条对称轴,则直线ax+by+c=0的倾斜角为多少度

Answer 1

假设tant=b/a,1/cost=√(a^2+b^2)/a

y=asinx+bcosx

=a(sinx+tantcosx)

=√(a^2+b^2)sin(x+t),x=π/6

x+t=π/2

t=π/3,arctana/b=π/6

ax+by+c=0的倾斜角

π-arctan(a/b)=5π/6