need help with trigonometry

Answer:
Step-by-step explanation:
Let us first find the hypotenuses of the right triangle.
[tex]c=\sqrt{12^2+9^2} =\sqrt{225} = 15[/tex]
[tex]sin(theta) = 12/15 = 4/5\\cos(theta) = 9/15 = 3/5\\tan(theta) = 12/9 = 4/3\\csc(theta) = sin(theta)^{-1} = 5/4\\sec(theta) = cos(theta)^{-1} = 5/3\\cot(theta) = tan(theta)^{-1} = 3/4[/tex]