Question

Given cosθ=√3/3 and sinθ<0. What is the value of sinθ?

Answer 1

`\sin^(2) \theta+\cos^(2) \theta=1 \\ \\ \sin^(2) \theta+\left((√(3))/(3) \right)^(2)=1 \\ \\ \sin^(2) \theta+(1)/(3)=1 \\ \\ \sin^(2) \theta=(2)/(3) \\ \\ \theta=-(√(2))/(√(3))=\boxed{-(√(6))/(3)}`