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This example illustrates how to apply the inverse trigonometric (Arc) functions to your transformations.

Info

NOTE: These functions are valid over specific ranges.

• Arcsine. See ASIN Function.
• Arccosine. See ACOS Function
• Arctangent. See ATAN Function.
• Arccotangent. Computed using ATAN function. See below.
• Arcsecant. Computed using ACOS function. See below.
• Arccosecant. Computed using ASIN function. See below.

Source:

In the following sample, input values are in radians. In this example, all values are rounded to two decimals for clarity.

Y
-1.00
-0.75
-0.50
0.00
0.50
0.75
1.00

Transformation:

Arcsine:

Valid over the range (-1 <= Y <= 1)

D trans
RawWrangle true 'asinY' step derive type: single value: round(degrees(asin(Y)), 2) as: 'asinY' Formula type Single row formula Formula round(degrees(asin(Y)), 2) New column name New formula

Arccosine:

Valid over the range (-1 <= Y <= 1)

D trans
RawWrangle true 'acosY' step derive type: single value: round(degrees(acos(Y)), 2) as: 'acosY' Formula type Single row formula Formula round(degrees(acos(Y)), 2) New column name New formula

Arctangent:

Valid over the range (-1 <= Y <= 1)

D trans
RawWrangle true 'atanY' step derive type: single value: round(degrees(atan(Y)), 2) as: 'atanY' Formula type Single row formula Formula round(degrees(atan(Y)), 2) New column name New formula

Arccosecant:

This function is valid over a set of ranged inputs, so you can use a conditional column for the computation. For more information, see ASIN Function.

D trans
RawWrangle true round(degrees(asin(divide(1, Y))), 2) step case condition: ifThenElse if: (Y <= -1) || (Y >= 1) then: round(degrees(asin(divide(1, Y))), 2) as: 'acscY' Condition type if...then...else If (Y <= -1) || (Y >= 1) Then 'acscY' New column name Conditional column

Arcsecant:

Same set of ranged inputs apply to this function. For more information, see ACOS Function.

D trans
RawWrangle true round(degrees(acos(divide(1, Y))), 2) step case condition: ifThenElse if: (Y <= -1) || (Y >= 1) then: round(degrees(acos(divide(1, Y))), 2) as: 'asecY' Condition type if...then...else If (Y <= -1) || (Y >= 1) Then 'asecY' New column name Conditional column

Arccotangent:

For this function, the two different ranges of inputs have different computations, so an `else` condition is added to the transformation. For more information, see ATAN Function.

D trans
RawWrangle true round(degrees(atan(divide(1, Y))), 2) case condition: ifThenElse if: Y > 0 then: round(degrees(atan(divide(1, Y))), 2) else: round(degrees(atan(divide(1, Y)) + pi()), 2) as: 'acotY' Condition type Then round(degrees(atan(divide(1, Y)) + pi()), 2) Conditional column step New column name if...then...else If Y > 0 'acotY' Else

Results:

YacotYasecYacscYatanYacosYasinY
-1.00-41.86180.00-90.00-45.00180.00-90.00
-0.75-49.99nullnull-37.00139.00-49.00
-0.50-60.29nullnull-27.00120.00-30.00
0.00nullnullnull0.0090.000.00
0.5063.44nullnull27.0060.0030.00
0.7553.13nullnull37.0041.0049.00
1.0045.000.0090.0045.000.0090.00