Answer:
(b) (2√5)/5
Step-by-step explanation:
You want to know the sine of the angle whose terminal point on the unit circle has a y-coordinate that is double its x-coordinate.
Tangent
The tangent of the angle is the ratio of the y-coordinate to the x-coordinate. The problem statement tells us that ratio is 2. The sin can be found from the tangent by ...
[tex]\sin\theta=\dfrac{\tan\theta}{\sqrt{\tan^2\theta+1}}\\\\\\\sin\theta=\dfrac{2}{\sqrt{2^2+1}}=\dfrac{2}{\sqrt{5}}\\\\\\\boxed{\sin\theta=\dfrac{2\sqrt{5}}{5}}\qquad\text{matches choice B}[/tex]
