Answer:
[tex]\frac{\sqrt{21} }{5}[/tex]
Step-by-step explanation:
Given
cosθ = - [tex]\frac{2}{5}[/tex]
Using the identity
sin²θ + cos²θ = 1 , then
sinθ = ± [tex]\sqrt{1-cos^20}[/tex]
= ± [tex]\sqrt{1-(-\frac{2}{5})^2 }[/tex]
= ± [tex]\sqrt{1-\frac{4}{25} }[/tex]
= ± [tex]\sqrt{\frac{21}{25} }[/tex]
= ± [tex]\frac{\sqrt{21} }{5}[/tex]
Since θ is in second quadrant the sinθ > 0 , thus
sinθ = [tex]\frac{\sqrt{21} }{5}[/tex]
