Answer:
see explanation
Step-by-step explanation:
Given
cotθ = [tex]\frac{4}{5}[/tex] = [tex]\frac{adjacent}{opposite}[/tex]
Use Pythagoras' identity to calculate the hypotenuse h
h² = 4² + 5² = 16 + 25 = 41 ( take square root of both sides )
h = [tex]\sqrt{41}[/tex]
θ is in quadrant III where sinθ < 0 and secθ < 0
sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = - [tex]\frac{5}{\sqrt{41} }[/tex] = - [tex]\frac{5\sqrt{41} }{41}[/tex]
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{4}{\sqrt{41} }[/tex]
secθ = [tex]\frac{1}{cos0}[/tex] = - [tex]\frac{\sqrt{41} }{4}[/tex]
