Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• 1 + tan²x = sec²x
• cot x = [tex]\frac{1}{tanx}[/tex]
Given
secΘ = [tex]\frac{4}{3}[/tex], then
tan²Θ = sec²Θ - 1 = ([tex]\frac{4}{3}[/tex] )² - 1 = [tex]\frac{16}{9}[/tex] - 1 = [tex]\frac{7}{9}[/tex], hence
tanΘ = ± [tex]\sqrt{\frac{7}{9} }[/tex] = ± [tex]\frac{\sqrt{7} }{3}[/tex]
Since 270° < Θ < 360° ← fourth quadrant where tanΘ < 0
Hence tanΘ = - [tex]\frac{\sqrt{7} }{3}[/tex]
and
cotΘ = [tex]\frac{1}{-\frac{\sqrt{7} }{3} }[/tex] = - [tex]\frac{3}{\sqrt{7} }[/tex] = - [tex]\frac{3\sqrt{7} }{7}[/tex]
