If 0 is an acute angle of the right triangle and if cos 0=5/13, then find the values of the remaining five trigonometric function for angle 0

See the highlighted values below.

Step-by-step explanation:

The following right angled triangle will have an angle whose cosine is 5/13.

Hypotenuse = 13 and the 2 legs will be 5 and 12 units long. The 12 is found using the Pythagoras theorem (13^2 = 5^2 + 12^2).

cos O = adjacent / hypotenuse = 5/13.

So sin O = opposite / hypotenuse = 12/13.

tan O = opposite / adjacent = 12/5.

csc O = 1 / sin O = 13/12.

sec O = 1 / cos O = 13/5.

cot O = 1 / tan O = 5/12.