They are all ratios for triangles found by dividing one side of a triangle by the others.
Ex: sine=opposite side/hypotenuse.
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This is so for a right-angled triangle. Non-right-angle triangle dimensions can be calculated by trigonometry but require more complicated derived formulae.
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Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
Yes, sine, cosine, tangent definitions are based on right triangles
Trigonometry
No, it does not.
The ratio of sine and cosine.