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NIST
4 Elementary FunctionsTrigonometric Functions

§4.17 Special Values and Limits

Table 4.17.1: Trigonometric functions: values at multiples of 112π.
θ sinθ cosθ tanθ cscθ secθ cotθ
0 0 1 0 1
π/12 142(3-1) 142(3+1) 2-3 2(3+1) 2(3-1) 2+3
π/6 12 123 133 2 233 3
π/4 122 122 1 2 2 1
π/3 123 12 3 233 2 133
5π/12 142(3+1) 142(3-1) 2+3 2(3-1) 2(3+1) 2-3
π/2 1 0 1 0
7π/12 142(3+1) -142(3-1) -(2+3) 2(3-1) -2(3+1) -(2-3)
2π/3 123 -12 -3 233 -2 -133
3π/4 122 -122 -1 2 -2 -1
5π/6 12 -123 -133 2 -233 -3
11π/12 142(3-1) -142(3+1) -(2-3) 2(3+1) -2(3-1) -(2+3)
π 0 -1 0 -1
4.17.1 limz0sinzz =1,
4.17.2 limz0tanzz =1.
4.17.3 limz01-coszz2 =12.