Trigonometric function for CNC

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 + 2*L* Tanθ

D-2*L* Tanθ

θ=

Tan-((D-d) / 2L)