The essence of trigonometric function is the mapping between any set of angles and a set of ratio variables. The usual trigonometric function is defined in a plane rectangular coordinate system. Its definition field is the whole real number field. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.

Extended data:

sin0=sin0 =0

cos0=cos0 = 1

tan 0 = tan 0 = 0 sin 15 = 0.650；

sin 15 =0.259

cos 15 =-0.759； cos 15 =0.966

tan 15 =-0.855； tan 15 =0.268

sin30 = 1/2

cos30 = 0.866

tan30 = 0.577

sin45 = 0.707

cos45 =0.707

tan 45 = 1.620； tan45 = 1

sin 60 =-0.305； sin60 =0.866

cos60 =-0.952； cos60 = 1/2

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