Spacing and Nonuse of the English Letter Indicator With Function Names and Their Abreviations:

a. A space must be left after a function name or its abbreviation. A space must be left even when the function name or its abbreviation is irectly followed by a sign of operation. The expression following the function name or its abbreviation must be spaced in accordance with its appropiate spacing rules.

No space should be left before a function name or its abbreviation unless it is preceded by a symbol requiring a space.

The English letter indicator must not be used with an English letter, a short-form combination, or a Roman numeral in regular type following a function or its abbreviation.

1. sin x
   

2. arc ab
   

3. Sine I
   

4. 
   

5. ctn -A = -ctn A
   

6. 1/cos -cos=tan * sin
   

7. 
   

8. 
   

9. y = 3tan 2x
   

10. 
    

11. y= 2sin x +3cos y
    

12. 2sin x +3cos y
    

13. sine x-sine y
    

14. 
    

15. 
    

16. 
    

17. 
    

18. 
    

19. 
    

20. 6sin 2A cos 4A
    

21. 
    

22. 
    

23. 
    

24. 
    

25. 
    

26. 
    

27. 
    

28. 
    

29. 
    

30. 
    

b. A space must be left between two or more consecutive abbreviated or unabbreviated function names unless they are clearly unspaced in the print text.

1. y = arc sin x
   

2. y = arcin x
   

3. What is the arc sine function?
   

4. Arc Sine x
   

5. 
   

6. 
   

7. 
   

8. cos arctan (-1)
   

9. cos[2 Arc csc (-7/5)]
   

10. The logarithm of sin 18* is written log sin 18*
    

Modifiers With Function Names: Modified function names must be transcribed according to the five-step rule for the transcription of modified expressions. When a function name or its abbreviation carries a modifier, The required space after the function name must follow the termination of the modifier.

However, the horizontal bar directly over or under the function name "lim" or "limit" must not be treated as a modifier. The symbols and must be used to denote "upper limit," and the symbols and must be used to denote "lower limit."

Superscripts and Subscripts With Function Names:

a. When a function name or its abbreviated carries a superscript or subscript, the required space after the function name must follow the superscript or subscript. A letter, numeral, or other mathematical expression following this space assumes the same level as the function name.

The superscript indicator must not be used when an abbreviated function name carries a mumeric superscript only on the first level below the baseline of writing. However, the subscript indicator must be used if an unabbreviated function name carries a numeric subscript.

1. sin²x
   

2. sine²x
   

3. sin²A+cos²(B+A)
   

4. 
   

5. 
   

6. (1-sin²x)² cos²x
   

7. 
   

8. 
   

9. log_n .125= -.6>
   

10. antilog_a x = N
    

11. 
    

12. log_2ex = -1.4
    

13. log₃ 81 = 4
    

14. log_.0543x = -.7
    

15. logarithm₃ 81 = 4
    

b. When a function name or its abbreviation occures in a superscript or subscript, the required space following it does not terminate the effect of the level indicator. In such cases, the space reinstates the level where the function name or its abbreviation appears. Thus, the letter, numeral, fraction, or other mathematical expression immediately following the space assumes the same levelas its related abbreviated or unabbreviated function name.

1. y = e^{sin x}
   

2. y = e^{sine x}
   

3. y = (sin x)^{tan x}
   

4. e^{ln x-2ln y}
   

5. e^{x+ln x}
   

6. y = e^cos2x
   

7. a^{g(x)log_af(x)}
   

8. 3^{log₃ 9}
   

9. e^{sin x}+e^{sin y}
   

10. 3^{log3 7}+2^{log₂ 5}
    

11. 2^{sec x} = y
    

12. a^{log_a x} = x
    

13. e^{sin x = a}>  y