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Definition of tangent

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2 Answers

For any point on the x-y plane, (x,y) = (r cos(θ), r sin(θ)), where the Initial Ray of θ is the positive x-axis and the Terminal Ray of θ starts at the origin and goes through (x,y).
 
r = √(x^2+y^2) is the distance from the origin to the point.
 
Then:
 
sin(θ) = y/r
cos(θ) = x/r
tan(θ) = sin(θ)/cos(θ) = y/x
cot(θ) = 1/tan(θ) = x/y
sec(θ) = 1/cos(θ) = r/x
csc(θ) = 1/sin(θ) = r/y