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9.7 Trigonometric functions
Whenever angles are included in your calculations or you perform coordinate transformations, you can use a variety of trigonometric functions in Gambas.
| Function | Description |
|---|---|
| Rad(Angle AS Float) AS Float | Converts the degree measure of an angle to radian measure. |
| Deg(Angle AS Float) AS Float | Converts the radians of an angle into degrees. |
| Pi([ Number AS Float] | Multiplies π with the value of Number and returns the product. If the optional argument Number is not set, the default value Number=1 is set. |
| Sin(Angle AS Float) | Calculates the sine of an angle. The angle must be specified in radian measure! The function value is within the interval[-1, +1]. |
| ASin(Number AS Float) AS Float or Asn(Number AS Float) AS Float | Calculates the radian measure of the angle at a given sine value. Note the periodicity of the sine function with the smallest period of 2π |
| Cos(Angle AS Float) AS Float | Calculates the cosine of an angle. The angle must be specified in radian measure! The function value is within the interval[-1, +1]. |
| ACos(Number AS Float) AS Float or Acs(Number AS Float) AS Float | Calculates the radian measure of the angle at a given cosine value. |
| Tan(Angle AS Float) | Calculates the tangent of an angle. The angle must be specified in radian measure! |
| ATan(Number AS Float) AS Float or Atn(Number AS Float) AS Float | Calculates the radian measure of the angle (interval[-π/2, +π/2]) to a given tangent value. |
| Mag(x AS Float, y AS Float) | This function calculates the distance of the point P(x, y) in the Cartesian coordinate system from the coordinate origin O(0,0) with Sqr(x*x+y*y*y). It is the same function as Hyp(). |
| Ang(x AS Float, y AS Float) | This function calculates the arc tangent of the two variables x and y. This corresponds to the calculation of the arc tangent of x/y, except that the algebraic sign of both arguments are used to determine the quadrant of the result. The function returns the function value in radian measure, which is between -π and +π (inclusive). This is the same function as ATan2(). |
| ASinh (Number AS Float) AS Float or Asnh(Number AS Float) AS Float | Calculates the hyperbolic arc sine to a given number. |
| Sinh(Number AS Float) | Calculates the hyperbolic sine to a given number. |
| ACosh(Number AS Float) AS Float or Acsh(Number AS Float) AS Float | Calculates the hyperbolic arc cosine to a given number. |
| Cosh(Number AS Float) AS Float | Calculates the hyperbolic cosine to a given number. |
| ATan (Number AS Float) AS Float or Atnh(Number AS Float) AS Float | Calculates the hyperbolic arc tangent of a number. |
| Tan (Number AS Float) | Calculates the hyperbolic tangent of a number. |
| ATan(y AS Float, x AS Float) AS Float or Atn2(y AS Float, x AS Float) AS Float | Calculates the arc tangent of the variable x and y. It corresponds to calculating the arc tangent of y/x, except that the sign of the two arguments are used to determine the quadrant of the result. The function returns a result between -π and +π (inclusive). Synonym for the function Ang(). |
| Hyp(x AS Float, y AS Float) AS Float | Synonym for the function Mag(x, y) |
Table 9.7.1: Overview of trigonometric functions
Hints:
- To convert Cartesian coordinates P(x,y) into polar coordinates P'(r,φ) use the function Mag(x,y) to calculate the distance r of the point P(x,y) from the coordinate origin O(0,0) = pole and the function Ang(x,y) to calculate the (polar) angle φ between radius r and the reference axis (pole axis). The (relative) unit length must be defined on the reference axis in units of length.
- You can do without the cosine function if you use the relationship sin²x + cos²x = 1 considering the quadrant relationships.
Examples:
- Is the tangent of the angle with radian measure = 1.33 smaller than the sinus of 50°?
- Calculate the angle ß (in degrees) whose cosine is 0.4432 and format the result with three decimal places and degrees!
- Is the distance of point P(8|6) from the coordinate origin O(0,0) greater than 9,8 units of length?
- Isn't sin(1) 90°?
- Enter the polar coordinates P'(r,a°) for point P (8|6) in the Cartesian coordinate system. Calculate the radian measure of the angle φ = 123° with three decimal places.
- Show that the cosine of (7/3)π is equal to 0.5!
Print IIf(Tan(1.33) - Sin(Rad(50)) < 0, "Yes", "No!")
Print Format(Deg(ACos(0.4432)), "#.###°")
Print IIf(Mag(8, 6) > 9.8, "Yes.", "No.")
Print Sin(1)
Print "P(8|6) ---> P'("; Hyp(8, 6); "|"; Deg(Ang(8, 6)); "°)"
Print "The arc measurement 123° = "; Round(Rad(123), -3)
Print "Cos(Pi(7/3)) = "; Cos(Pi(7/3))
No! 63,692° Yes. 0,8414709848079 P(8|6) ---> P'(10|36,87°) The arc measurement Rad(123°) = 2,147 Yes - Cos(Pi(7/3)) = 0,5
k9/k9.7/start.txt · Last modified: 11.02.2022 (external edit)
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