Request for MathCat pronunciation to differentiate between arcsinh vs. arcsin, and arctanh vs. arctan. Currently, they sound the same.

まず、リンク先の逆双曲線関数のページにある Exercise 2 のエントリ C から H を使い、スクリーンリーダーで MathCATForPython の発音を再現します。arcsinh と arctanh の US 英語の発音規則を見つけ、他のロケールを変更せずに、要求された「arksinch」と「ahrk tahnsh」の区別を検証します。指定された US 英語シンセサイザーの動作で、これらの用語が arcsin と arctan から聴覚的に区別できれば完了です。

Request for MathCat pronunciation to differentiate between arcsinh vs. arcsin, and arctanh vs. arctan. Currently, they sound the same.

1. With a screen-reader, go to this page:
   https://complexanalysis.org/web/sec_inverse-trig-hyperbolics.html on inverse hyperbolic functions.
2. Refer to Exercise 2, entries C through H on this page for examples.
   PROBLEM: There are several mathematical terms which synthesizers pronounce the same regardless of context.
   EXPECTED: pronunciations need to be different based on context. This request is for US English only.

“Hyperbolic arcsinh” is pronounced simply as “arcsin” but should be pronounced phonetically as “arksinch” for clarity and to bring it into parity with sinh, which is pronounced “sinch.”
“arctanh” now is pronounced “arctan,” but should be pronounced as “ahrk tahnsh”
for clarity and parity with tanh sounding as “tahnsh.”

[With SAPI 5 64-bit [MS Zira US] synth, using Dictionary manager, the best phonetic spelling is ark tansh and ark sinch. Phonetic spelling may differ between synths]

NOTE: when looking for the correct pronunciations, these are the sources used:

Finding out the correct pronunciations, I used these sources:

Correct Pronunciation of “sinh” (Hyperbolic Sine) In mathematics, sinh is the abbreviation for the hyperbolic sine function, defined as:

When pronouncing sinh, there are several common variants, but the most widely accepted in the U.S. is:

/ˈsɪntʃ/ — “sinch” (as in “cinch”), with the “sh” sound and the “ch” as in “China” Mathwords+1.
Other common pronunciations you might hear include:

/ˈʃaɪn/ — “shine” (British-influenced, common in some academic or informal
contexts) Mathematics Stack Exchange+1.

/ˈsɪn h/ — “sine H” (breaking it into “sine” + “H”), which is clear and avoids confusion with trigonometric sine Mathematics Stack Exchange.

Correct Pronunciation of "arctanh"
The correct pronunciation of arctanh in US English is:

/ˈɑː(ɹ)kˌtænʃ/ — “ah‑rtahn‑sh” Wiktionary+1.

Breakdown
/ˈɑː/ — “ah” (long “a” sound, like in father)
(ɹ) — optional alveolar approximant “r” sound (common in American English) /k/ — “k” sound /ˌtænʃ/ — “tahn‑sh” (short “a” in tan, plus the “sh” sound)