Aan angle in quadrant I, the value of sin[tex]\theta[/tex] is [tex]\rm Sin \theta=\dfrac{\sqrt{14} }{5}[/tex].
Sin theta is defined as the ratio of perpendicular and hypotenuse.
The given equation is;
[tex]\rm Cos\theta=\dfrac{\sqrt{11} }{5}[/tex]
The cos[tex]\theta[/tex] is given by;
[tex]\rm Cos\theta=\dfrac{Base}{hypotenuse}[/tex]
By applying Pythagoras theorem the value of base is;
[tex]\rm (5)^2=Perpendicular^2+ (\sqrt{11} )^2\\\\ Perpendicular^2= 25-11\\\\ Perpendicular^2=14\\\\ Perpendicular =\sqrt{14}[/tex]
The value of sin[tex]\theta[/tex] is;
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypoteunse}\\\\Sin \theta=\dfrac{\sqrt{14} }{5}[/tex]
Hence, the value of sin[tex]\theta[/tex] is [tex]\rm Sin \theta=\dfrac{\sqrt{14} }{5}[/tex].
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