Answer:
sinΘ = [tex]\frac{15}{17}[/tex]
Step-by-step explanation:
Using the trigonometric identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
cosΘ = [tex]\frac{8}{17}[/tex], then
sinΘ = ± [tex]\sqrt{1-(8/17)^2}[/tex] = ± [tex]\sqrt{1-\frac{64}{289} }[/tex] = ± [tex]\sqrt{\frac{225}{289} }[/tex] = ± [tex]\frac{15}{17}[/tex]
Since Θ is in first quadrant then sinΘ > 0, thus
sinΘ = [tex]\frac{15}{17}[/tex]
