Answer:
C.
Step-by-step explanation:
In trigonometry, we have an equation as following:
[tex]sine^{2} x + cosine^{2} x = 1[/tex]
Replace θ into the above equation, we would have:
(sine θ)^2 + (cosine θ)^2 = 1
=> (sine θ)^2 = 1 - (cosine θ)^2 (1)
As given, we have cosine θ = -3/7. Replace it into the equation (1), we have:
(sine θ)^2 = 1 - (-3/7)^2
=>(sine θ)^2 = 1 - 9/49 = 40/49
=> sine θ = ±[tex]\sqrt{\frac{40}{49} }[/tex] = ±[tex]\frac{2\sqrt{10} }{7}[/tex]
So sine θ = [tex]\frac{2\sqrt{10} }{7}[/tex] or sine θ = - [tex]\frac{2\sqrt{10} }{7}[/tex]
However, as θ is in quadrant II, sine θ has a positive value
=> sine θ = [tex]\frac{2\sqrt{10} }{7}[/tex]
So that the correct answer is C
