Answer:
tanΘ = - [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Using the trigonometric identities
• sin²x + cos²x = 1, hence
cosx = ± √(1 - sin²x )
• tanx = [tex]\frac{sinx}{cosx}[/tex]
given sinΘ = [tex]\frac{12}{13}[/tex], then
cosΘ = ± [tex]\sqrt{1-(12/13)^2}[/tex]
Since Θ is in the second quadrant where cosΘ < 0, then
cosΘ = - [tex]\sqrt{1-\frac{144}{169} }[/tex]
= - [tex]\sqrt{\frac{25}{169} }[/tex] = - [tex]\frac{5}{13}[/tex]
tanΘ = [tex]\frac{\frac{12}{13} }{\frac{-5}{13} }[/tex]
= [tex]\frac{12}{13}[/tex] × - [tex]\frac{13}{5}[/tex] = - [tex]\frac{12}{5}[/tex]
