Answer:
tanΘ = - [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Using the trigonometric identity
tan²Θ + 1 = sec²Θ, thus
tan²Θ + 1 = ([tex]\frac{13}{5}[/tex] )² = [tex]\frac{169}{25}[/tex] ( subtract 1 from both sides )
tan²Θ = [tex]\frac{144}{25}[/tex] ( take the square root of both sides )
tanΘ = ± [tex]\sqrt{\frac{144}{25} }[/tex]
Since 270 < Θ < 360 , that is the fourth quadrant where tan Θ < 0, thus
tanΘ = - [tex]\frac{12}{5}[/tex]
