Given:
The terminal point of [tex]\theta[/tex] is [tex]\left(\dfrac{1}{2},\dfrac{\sqrt{3}}{2}\right)[/tex].
To find:
The value of [tex]\sin \theta[/tex].
Solution:
If the terminal point of [tex]\theta[/tex] is [tex](x,y)[/tex], then
[tex]\sin \theta = \dfrac{y}{\sqrt{x^2+y^2}}[/tex]
The terminal point of [tex]\theta[/tex] is [tex]\left(\dfrac{1}{2},\dfrac{\sqrt{3}}{2}\right)[/tex]. So,
[tex]\sin \theta = \dfrac{\dfrac{\sqrt{3}}{2}}{\sqrt{\left(\dfrac{1}{2}\right)^2+\left(\dfrac{\sqrt{3}}{2}\right)^2}}[/tex]
[tex]\sin \theta = \dfrac{\dfrac{\sqrt{3}}{2}}{\sqrt{\dfrac{1}{4}+\dfrac{3}{4}}}[/tex]
[tex]\sin \theta = \dfrac{\dfrac{\sqrt{3}}{2}}{\sqrt{1}}[/tex]
[tex]\sin \theta = \dfrac{\dfrac{\sqrt{3}}{2}}{1}[/tex]
[tex]\sin \theta =\dfrac{\sqrt{3}}{2}[/tex]
Therefore, the correct option is B.
