Question

已知角a的终边在x+y=0上,则2sina+cosa

Answer 1

当角的终边在第二象限时,a=3π/4+2kπ,k∈Z.

2sina+cosa=2sin(3π/4+2kπ)+cos(3π/4+2kπ)

=2sin(3π/4)+cos(3π/4)

=√2-√2/2

=√2/2

当角的终边在第四象限时,a=-π/4+2kπ,k∈Z.

2sina+cosa=2sin(-π/4+2kπ)+cos(-π/4+2kπ)

=2sin(-π/4)+cos(-π/4)

=-√2+√2/2

=-√2/2

所以2sina+cosa=√2/2或-√2/2