We first need to find the hypotenuse because several trigonometric functions require the hypotenuse in its ratio (like sin and cos).
We can do this by applying Pythagorean theorem since we have the side lengths a and b.
hypotenuse = [tex]\sqrt{12^2+5^2}[/tex] = 13
Now we can solve for the 6 functions!
sin Θ = opp/hyp = 12/13
cos Θ = adj/hyp = 5/13
tan Θ = opp/adj = 12/5
csc Θ = 1/(sin Θ)= 1/(opp/hyp) = hyp/opp = 13/12
sec Θ = 1/(cos Θ) = 1/(adj/hyp) = hyp/adj = 13/5
cot Θ = 1/(tan Θ) = 1/(opp/adj) = adj/opp = 5/12
Let me know if you have any questions!
