No, it does not.
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Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
For finding the angles in a right angled triangle the ratios are: sine = opposite divided by the hypotenuse cosine = adjacent divided by the hypotenuse tangent = opposite divided by the adjacent
No, it is not. To be correct, the expression requires parenthesis, which are missing.
Yes, sine, cosine, tangent definitions are based on right triangles
That is the correct spelling of "tangent" (intersecting at one point, or sine divided by cosine, or opposite side over adjacent side).