sina=1/3,sin(a+b)=1,求sin(2a+3b)的值

Question

sina=1/3,sin(a+b)=1,求sin(2a+3b)的值

Answer 1

∵sin(a+b)=1
∴ a+b=2kπ+π/2,k∈Z
3(a+b)=6kπ+3π/2,k∈Z
∴ sin(2a+3b)
=sin[3(a+b)-a]
=sin(6kπ+3π/2-a)
=sin(3π/2-a)
=-cosa
=±√(1-sin²a)
=±√(8/9)
=±2√2/3