Simple vector calculator
Simplify your components functions:


def fxcomponent(x, angle):
    return x * math.cos(math.radians(angle))

def fycomponent(y, angle):
    return y * math.sin(math.radians(angle))



Instead of using number.lower() in every IF statement, convert it once putting number = number.lower() after get the value from input.'
Focusing on readability and maintainability you should extract the copy+paste code of calculating x and y and create a generic function that encapsulates that. So, your code will look like this:


def calculate_fcomponent(component):
    print ('Please tell me the %c and the angle:' % (component))
    value, angle = [int(x) for x in input('&gt;').split()]
    result = fxcomponent(value, angle) if component == 'x' else fycomponent(value, angle)
    print ('The %c component of %d at %d° is: %d' % (component, value, angle, result))
    print()

def run():
    print('Welcome to my Python vector components calculator!')
    print()

    prompt = ('Please select what you wish to find:'
              '\n-type x for x-component'
              '\n-type y for y-component'
              '\n-type quit to end program')

    flag = True 

    while flag:
        cmd = input(prompt + '\n&gt;')
        cmd = cmd.lower()

        if cmd == 'quit':
            flag = False

        elif cmd in ('x', 'y'):
            calculate_fcomponent(cmd)

        else:
            print ('Invalid command; try again!')

if __name__ == "__main__":
    run()