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Appendix I / Utilities / Trigonometrical Functions
_ _
Both approximations result in errors similar to the sine function with
different phasing as shown in
Figure 2-7.
22.11.3 Tangent Approximation
THT_AT [degrees]
-10
-15
-20
-25
-30
-35
-40
0 10 20 30
TIME [seconds]
40 50 60
22.11-3
TGT_003.mtb
TGT_007.mtb
TAN_F takes angle (XI) in the range [-2π , 2π], and returns its tangent.
y
: = TAN_F
2
10.
50496 ⋅ X ⋅
( ) ( 1 − X )
XI
: =
2
ξ ⋅ ( 3.
34485 − X )
2 −8
2
( 1 − 4 ⋅ X ) ≥ 10 ⇒ ξ : = 1 − 4 ⋅ X
1
1
Equation 22.11-9
Equation 22.11-10
2 −8
−8
2
( 1 − 4 ⋅ X ) < 10 ⇒ ξ : = 10 ⋅ sign ( 1 − 4 ⋅ X )
⎧ ⎡ 3 ⋅ π ⎤ ⎡ π ⎤ ⎫
XI ∈ ⎨ ⎢ π ,
, ⎬ ⇒ X I
⎩ 2 ⎥ ∪ ⎢ − π −
⎣ ⎦ ⎣ 2 ⎥
⎦ ⎭
⎧ ⎡ 3 ⋅ π ⎤ ⎡ π ⎤ ⎫
XI ∈ ⎨ ⎢ − , − π ∪ , ⎬ ⇒ X I
⎩ 2 ⎥ ⎢ π
⎣ ⎦ ⎣ 2 ⎥
⎦ ⎭
1
Equation 22.11-11
( X ) → [ 0 , π 2 ]
Equation 22.11-12
( X ) → [ − π 2 , 0 ]
Equation 22.11-13