William Anthony Granville

“ XXIV ∴ . ↑ Graph of arc sin vIt should be remembered that this function is defined only for values of between -1 and +1 inclusive and that (the function) is many-valued, there being infinitely many arcs whose sines will equal . Thus, in the figure (the locus of ) , when .
In the above discussion, in order to make the function single-valued; only values of between and inclusive (points on arc ) are considered; that is, the arc of smallest numerical value whose sine is .
↑ Graph of arc cos vThis function is defined only for values of between -1 and +1 inclusive, and is many-valued. ”

“ Differentiate the following:
1. . by XI [.] 2. . by XIII [.] . . 3. . This may also be written, . by VI [ and .] by XII 4. . by V [ and .] by VI and XI . 5. . Ans. . 6. . . 7. . . 8. . . 9. . . 10. . 11. . . 12. . 13. . 14. . . 15. . ”