An introduction to the study of the elements of the differential and integral calculus. From the German of the late Axel Harnack, With the permission of the author.

~ 12-14. Trigonometric and Circular. 23
Cos-' y denotes that number between 0 and zt whose cosine is y.
(- 1 y< 1).
Tan-' y denotes that number between - I t and I- t whose tangent is y.
(- oo<y + oo).
Cot- y denotes that number between 0 and it whose cotangent is y.
(- oo y < + o).
14. Algebraic functions and the four simple kinds of transcendentals: Exponential and Trigonometric functions with their
inverses: Logarithmic and Circular functions, form in their innumerable combinations the proximate object of analytical investigation.
Its course which is aimed at the actual calculation of the functions
and at the knowledge of their properties, will reveal a close relation
between exponential and trigonometric functions, and therefore also
between the logarithm and the circular function. Further it will appear,
that the operations of the Differential Calculus, when applied to these
functions do not give rise to new ones, but that on the other hand, the
Integral Calculus does teach us to exhibit and calculate new functions.