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Appendix I / Utilities / Trigonometrical Functions
_ _
TAN_F ERROR
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
x 10-3
1
-1
0 10 20 30 40 50 60 70 80 90
ANGLE (DEGREES)
Figure 22-12 : Tangent Function Error
[ − 2 ⋅ π , − 3 ⋅ π 2 ] ⇒ X ( X ) → [ 0 , π 2 ]
XI ∈
I
22.11-4
Equation 22.11-14
[ 3 ⋅ π 2 , 2 ⋅ π ] ⇒ X ( X ) → [ − π 2 , 0 ]
XI ∈
I
Equation 22.11-15
The error in this function is [-0.02 , 0.02] for inputs [0° , 85.8°] as shown in
Figure 22-12.
22.11.4 Arc-sine Approximation
ASIN_F takes the sine of (XI) in the range [-1 , 1] and returns (XI) in the
range [-π , π].
y
: = ASIN_F
2
XI
⋅ ( 4.
13564 − 2.
49527 ⋅ 1 − XI
)
( X ) : =
I
1.
63755 + X
2
I
Equation 22.11-16
If the input is outside the specified input range it is truncated to sign (1 , XI).
The error in this function is [-0.15° , 0.15°] as shown in Figure 22-13.
22.11.5 Arc-cosine Approximation
ACOS_F takes the cosine of (XI) in the range ]-1 , 1[ and returns (XI) in the
range ]-π , π[ .
( X ) : = ( π 2 ) ( X )
y : = ACOS_F − ASIN_F
I
I
Equation 22.11-17