sec ф = 5/3 (quadrant 4)
let x = base
y = perp
z = hypotenuse
sec ф = hypotenuse/base = 5/3
⇒ z = 5 and x = 3
finding y:
z² = x² + y²
5² = 3² + y²
y² = 25-9
y² = 16
y = 4
now finding all other geometric functions of theta:
sin ф = y/z = 4/5
sin ф = -4/5 (sin is negative in the 4th quadrant)
cos ф = x/z = 3/5
cos ф = 3/5 (cos is positive in 4th quadrant)
tan ф = y/x = 4/3
tan ф = -4/3 (tan is negative in 4th quadrant)
cosec ф = z/y = 5/4
cosec ф = -5/4 (cosec is negative in the 4th quadrant)
cot ф = x/y = 3/4
tan ф = -3/4 (tan is negative in 4th quadrant)