Answer:
sinΘ = - [tex]\frac{\sqrt{33} }{7}[/tex]
Step-by-step explanation:
Using the trigonometric identity
sin²Θ + cos²Θ = 1, thus
sinΘ = ± [tex]\sqrt{1-cos^20}[/tex]
Since Θ is in the fourth quadrant then sinΘ < 0
Given
cosΘ = [tex]\frac{4}{7}[/tex] , then
sinΘ = - [tex]\sqrt{1-(\frac{4}{7})^2 }[/tex] = - [tex]\sqrt{1-\frac{16}{49} }[/tex] = - [tex]\sqrt{\frac{33}{49} }[/tex] = - [tex]\frac{\sqrt{33} }{7}[/tex]
