When trying to remember the ratio for each trigonometric function, sine, cosine, tangent, cotangent, secant and cosecant, we really only need to know sine, cosine and tangent. Once we know them, cotangent, secant and cosecant are the recipricol of tangent, cosine and sine, respectively.
In a right triangle, the sine of an angle is the length side opposite the angle divided by the length of the hypotenuse (the side opposite the right angle).
Cosine is the length of the side adjacent to the angle divided by the length of the hypotenuse.
Tangent is the length of the side opposite divided by the length of the side adjacent.
Sine = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
Cotangent = 1/tangent
Secant = 1/cosine
Cosecant = 1/sine
Notice that tangent is sine/cosine