Answer:
See explanation
Step-by-step explanation:
Point with coordinates (12,5) lies on the distance
[tex]d=\sqrt{(12-0)^2 +(5-0)^2}=\sqrt{144+25}=13[/tex]
from the origin.
Consider right triangle with vertices at the origin, at the given point (12,5) and at it projection on the x- axis (point (12,0)).
Hence,
Hypotenuse = 13 units
Adjacent to the angle leg = 12 units
Opposite to the angle leg = 5 units
By the definition of trigonometric functions,
[tex]\sin \theta=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{5}{13}\\ \\\cos \theta=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{12}{13}\\ \\\tan \theta=\dfrac{\text{Opposite leg}}{\text{Adjacent leg}}=\dfrac{5}{12}\\ \\\cot \theta=\dfrac{\text{Adjacent leg}}{\text{Opposite leg}}=\dfrac{12}{5}\\ \\\csc \theta=\dfrac{\text{Hypotenuse}}{\text{Opposite leg}}=\dfrac{13}{5}\\ \\\sec \theta=\dfrac{\text{Hypotenuse}}{\text{Adjacent leg}}=\dfrac{13}{12}[/tex]
