Angle function relationship
(Sine)
Sin θ = Opposite side A / Hypotenuse C
(Cosine)
Cosθ = adjacent side B / hypotenuse C
(Tangent)
Tanθ = Opposite side A / Adjacent side B

Opposite side A
= Hypotenuse C * Sinθ
Opposite side A
= Adjacent side B * Tanθ
Neighbor B
= Hypotenuse C * Cosθ
Neighbor B
= Opposite side A / Tanθ
Hypotenuse C
= Opposite side A / Sinθ
Hypotenuse C
= Adjacent side B / Cosθ
Example: It is known that the hypotenuse C=20,
Angle θ=35 degrees, find the opposite side A and the adjacent side B

　　　 Opposite side A
= Hypotenuse C * Sinθ = 20 * Sin (35) = 20 * 0.573576 = 11.471

　　　Neighbor B
= Hypotenuse C * Cosθ = 20 * Cos (35) = 20 * 0.81915 = 16.383
The relationship between taper of general lathe and trigonometric function
　
Taper ratio T=(large diameter D-small diameter d)
/ (Length L)
Tanθ=
(Large diameter D-small diameter d) / (2*length L)
D=
d + 2*L* Tanθ
d=
D-2*L* Tanθ
θ=
Tan-((D-d) / 2L)