Trigonometric Functions Using Degree
Problem Statement
Trigonometric functions (i.e., sin(x) and cos(x)) use radian for their argument. Using modules, you can design your own trigonometric functions that use degree. Write a module that contains functions for converting radian to degree and degree to radian and sin(x) and cos(x) with arguments in degree rather than in radian.
Solution
The following is the desired module:
! --------------------------------------------------------------------
! MODULE MyTrigonometricFunctions:
! This module provides the following functions and constants
! (1) RadianToDegree() - converts its argument in radian to
! degree
! (2) DegreeToRadian() - converts its argument in degree to
! radian
! (3) MySIN() - compute the sine of its argument in
! degree
! (4) MyCOS() - compute the cosine of its argument
! in degree
! --------------------------------------------------------------------
MODULE MyTrigonometricFunctions
IMPLICIT NONE
REAL, PARAMETER :: PI = 3.1415926 ! some constants
REAL, PARAMETER :: Degree180 = 180.0
REAL, PARAMETER :: R_to_D = Degree180/PI
REAL, PARAMETER :: D_to_R = PI/Degree180
CONTAINS
! --------------------------------------------------------------------
! FUNCTION RadianToDegree():
! This function takes a REAL argument in radian and converts it to
! the equivalent degree.
! --------------------------------------------------------------------
REAL FUNCTION RadianToDegree(Radian)
IMPLICIT NONE
REAL, INTENT(IN) :: Radian
RadianToDegree = Radian * R_to_D
END FUNCTION RadianToDegree
! --------------------------------------------------------------------
! FUNCTION DegreeToRadian():
! This function takes a REAL argument in degree and converts it to
! the equivalent radian.
! --------------------------------------------------------------------
REAL FUNCTION DegreeToRadian(Degree)
IMPLICIT NONE
REAL, INTENT(IN) :: Degree
DegreeToRadian = Degree * D_to_R
END FUNCTION DegreeToRadian
! --------------------------------------------------------------------
! FUNCTION MySIN():
! This function takes a REAL argument in degree and computes its
! sine value. It does the computation by converting its argument to
! radian and uses Fortran's sin().
! --------------------------------------------------------------------
REAL FUNCTION MySIN(x)
IMPLICIT NONE
REAL, INTENT(IN) :: x
MySIN = SIN(DegreeToRadian(x))
END FUNCTION MySIN
! --------------------------------------------------------------------
! FUNCTION MySIN():
! This function takes a REAL argument in degree and computes its
! cosine value. It does the computation by converting its argument to
! radian and uses Fortran's cos().
! --------------------------------------------------------------------
REAL FUNCTION MyCOS(x)
IMPLICIT NONE
REAL, INTENT(IN) :: x
MyCOS = COS(DegreeToRadian(x))
END FUNCTION MyCOS
END MODULE MyTrigonometricFunctions
Click here to download this program.
Here is the main program:
! -----------------------------------------------------------------------
! PROGRAM TrigonFunctTest:
! This program tests the functions in module MyTrigonometricFunctions.
! Module MyTrigonometricFunctions is stored in file trigon.f90.
! Functions in that module use degree rather than radian. This program
! displays the sin(x) and cos(x) values for x=-180, -170, ..., 0, 10, 20,
! 30, ..., 160, 170 and 180. Note that the sin() and cos() function
! in module MyTrigonometricFunctions are named MySIN(x) and MyCOS(x).
! -----------------------------------------------------------------------
PROGRAM TrigonFunctTest
USE MyTrigonometricFunctions ! use a module
IMPLICIT NONE
REAL :: Begin = -180.0 ! initial value
REAL :: Final = 180.0 ! final value
REAL :: Step = 10.0 ! step size
REAL :: x
WRITE(*,*) 'Value of PI = ', PI
WRITE(*,*)
x = Begin ! start with 180 degree
DO
IF (x > Final) EXIT ! if x > 180 degree, EXIT
WRITE(*,*) 'x = ', x, 'deg sin(x) = ', MySIN(x), &
' cos(x) = ', MyCOS(x)
x = x + Step ! advance x
END DO
END PROGRAM TrigonFunctTest
Click here to download this program. Program Input and Output
The following is the output from the above program.Value of PI = 3.1415925 x = -180.deg sin(x) = 8.742277657E-8 cos(x) = -1. x = -170.deg sin(x) = -0.173648298 cos(x) = -0.98480773 x = -160.deg sin(x) = -0.342020214 cos(x) = -0.939692616 x = -150.deg sin(x) = -0.50000006 cos(x) = -0.866025388 x = -140.deg sin(x) = -0.642787635 cos(x) = -0.766044438 x = -130.deg sin(x) = -0.766044438 cos(x) = -0.642787635 x = -120.deg sin(x) = -0.866025388 cos(x) = -0.50000006 x = -110.deg sin(x) = -0.939692616 cos(x) = -0.342020124 x = -100.deg sin(x) = -0.98480773 cos(x) = -0.173648193 x = -90.deg sin(x) = -1. cos(x) = -4.371138829E-8 x = -80.deg sin(x) = -0.98480773 cos(x) = 0.173648223 x = -70.deg sin(x) = -0.939692616 cos(x) = 0.342020154 x = -60.deg sin(x) = -0.866025448 cos(x) = 0.49999997 x = -50.deg sin(x) = -0.766044438 cos(x) = 0.642787635 x = -40.deg sin(x) = -0.642787576 cos(x) = 0.766044438 x = -30.deg sin(x) = -0.5 cos(x) = 0.866025388 x = -20.deg sin(x) = -0.342020124 cos(x) = 0.939692616 x = -10.deg sin(x) = -0.173648179 cos(x) = 0.98480773 x = 0.E+0deg sin(x) = 0.E+0 cos(x) = 1. x = 10.deg sin(x) = 0.173648179 cos(x) = 0.98480773 x = 20.deg sin(x) = 0.342020124 cos(x) = 0.939692616 x = 30.deg sin(x) = 0.5 cos(x) = 0.866025388 x = 40.deg sin(x) = 0.642787576 cos(x) = 0.766044438 x = 50.deg sin(x) = 0.766044438 cos(x) = 0.642787635 x = 60.deg sin(x) = 0.866025448 cos(x) = 0.49999997 x = 70.deg sin(x) = 0.939692616 cos(x) = 0.342020154 x = 80.deg sin(x) = 0.98480773 cos(x) = 0.173648223 x = 90.deg sin(x) = 1. cos(x) = -4.371138829E-8 x = 100.deg sin(x) = 0.98480773 cos(x) = -0.173648193 x = 110.deg sin(x) = 0.939692616 cos(x) = -0.342020124 x = 120.deg sin(x) = 0.866025388 cos(x) = -0.50000006 x = 130.deg sin(x) = 0.766044438 cos(x) = -0.642787635 x = 140.deg sin(x) = 0.642787635 cos(x) = -0.766044438 x = 150.deg sin(x) = 0.50000006 cos(x) = -0.866025388 x = 160.deg sin(x) = 0.342020214 cos(x) = -0.939692616 x = 170.deg sin(x) = 0.173648298 cos(x) = -0.98480773 x = 180.deg sin(x) = -8.742277657E-8 cos(x) = -1.
Discussion
- Module MyTrigonometricFunctions defines four constants:
- PI,
- Degree180,
- R_to_D for radian to degree conversion, and
- D_to_R for degree to radian conversion.
- Module MyTrigonometricFunctions contains four functions:
- RadianToDegree() converts its radian argument to degree;
- DegreeToRadian() converts its degree argument to radian;
- MySIN() takes a degree argument and returns its sine value; and
- MyCOS() takes a degree argument and returns its cosine value.
- In the module, MySIN(x) first converts its degree argument x to radian using function DegreeToRadian() and supplies the result to the Fortran SIN() function for computing the value of sine.
- The module uses MySIN() and MyCOS() rather than the same Fortran names SIN() and COS() to avoid confusion.
- As described in the use of modules, the main program can use variables, PARAMETERs and functions declared and defined in a module. Thus, the main program can use the value of PARAMETER PI defined in module MyTrigonometricFunctions. This is why there is no declaration of PI in the main program.
- In the main program, REAL variable x starts with 180 (in degree) and steps through 180 (in degree) with a step size 10. For each value of x, its SIN() and COS() is computed.
- If the main program and module MyTrigonometricFunctions are stored in files trigon.f90 and tri-test.f90, respectively, then you can compile them together with the following command:
or with the following that generates an executable called tri-test:f90 trigon.f90 tri-test.90
f90 trigon.f90 tri-test.90 -o tri-test
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