Find tangent from other two trig ratios

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I understand the six trig ratios, and know that tangent= opposite/adjacent. I feel like, on a website, I've seen people use either cosine/sine or sine/cosine (can't remember which) to find the tangent.

Is one of these two (cos/sin or sin/cos) valid/does it work?

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The definition of tangent

$$\tan{x} = \frac{\sin{x}}{\cos{x}}$$

is what they are referring to.

Similarly, the other trigonometric ratios are defined as follows $$\cot{x} = \frac{\cos{x}}{\sin{x}} \\ \sec{x} = \frac{1}{\cos{x}} \\ \csc{x} = \frac{1}{\sin{x}}$$