Definition of tangent

Question

I need definitions

Answer 1

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

Answer 2

Go to the link below for a quick guide to the definitions and identities of the trig functions, including the tangent.

 

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf