Learn Hardcore Danish: Hosten forsvinder langsomt, når medicinen virker, og værelset er varmt. - The cough disappears slowly when the medicine works and the room is warm.

So Hosten forsvinder… literally means “The cough disappears…”.
Using plain hoste here would sound like you’re talking about cough in general, not a specific one the person has.

Why is the verb forsvinder used here, and what exactly does it mean?

forsvinder is the present tense of forsvinde, which means to disappear / to vanish.

forsvinde (infinitive) – to disappear
forsvinder (present) – disappears / is disappearing
forsvandt (past) – disappeared

In this sentence it’s describing what happens to the cough over time: it disappears (goes away).

Colloquially, Danes also say:

Hosten går væk langsomt – The cough goes away slowly.

forsvinde is a bit more neutral/formal than gå væk, but both are common.

Why is langsomt at the end: Hosten forsvinder langsomt and not Hosten langsomt forsvinder?

langsomt is an adverb describing how the cough disappears.

Default word order in a simple main clause is:

Subject – Verb – (Objects/Adverbs)

So:

Hosten (subject)
forsvinder (verb)
langsomt (adverb)

Hosten langsomt forsvinder sounds wrong in standard Danish. The adverb usually comes after the main verb in such a simple clause.

Why is it langsomt and not langsom or langsomme?

Danish often forms adverbs from adjectives by adding -t:

langsom (adjective) – slow
langsomt (adverb) – slowly

You use:

langsom in front of a noun:
- en langsom bus – a slow bus
langsom/langsomt as a predicative adjective (after er, bliver etc.), depending on gender/number:
- Bussen er langsom. – The bus is slow.

But when you describe how something happens (i.e. an adverb), you use langsomt:

Hosten forsvinder langsomt. – The cough disappears slowly.

Why is it når and not da or hvis?

All three can be translated by when/if in English, but they’re used differently:

når = when / whenever (repeated, general, or future time)
- Hosten forsvinder, når medicinen virker…
  = whenever / when the medicine works…
da = when (one specific event in the past)
- Hosten forsvandt, da medicinen virkede.
  = the cough disappeared when the medicine worked (that time).
hvis = if (condition, not time)
- Hosten forsvinder, hvis medicinen virker.
  = the cough disappears if the medicine works.

In your sentence we’re talking about the general situation or a condition that’s tied to time, so når is the natural choice.

Why is the present tense used: forsvinder, virker, er instead of future forms?

Danish uses the present tense much more than English to talk about:

general truths
habitual situations
future events introduced by når (when)

So:

Hosten forsvinder, når medicinen virker…
Literally: The cough disappears when the medicine works…
Natural English: The cough will disappear when the medicine works…

You could add vil to make an explicit future:

Hosten vil forsvinde, når medicinen virker…

But it’s not necessary; the present tense already implies a future result in this kind of når-clause construction.

How does word order work after når in når medicinen virker?

After når, you have a subordinate clause, and in subordinate clauses Danish has subject before verb:

når medicinen virker
- medicinen (subject)
- virker (verb)

You cannot invert here:

✗ når virker medicinen (wrong in this context)

Compare:

Main clause question (inversion allowed/required):
- Hvornår virker medicinen? – When does the medicine work?
Subordinate clause (no inversion):
- Jeg ved ikke, hvornår medicinen virker. – I don’t know when the medicine works.

Why is there a comma before når: …, når medicinen virker, og værelset er varmt.?

Danish comma rules are a bit different from English, but in modern recommended usage:

You put a comma before most subordinate clauses introduced by words like når, at, fordi, som.

So:

Hosten forsvinder langsomt, når medicinen virker…

The comma marks the start of the subordinate når-clause.
The extra comma before og værelset er varmt is optional and depends on which comma system you follow; in current common practice, many would write:

Hosten forsvinder langsomt, når medicinen virker og værelset er varmt.

Both versions are seen; for a learner, it’s enough to know that a comma before “når” is standard.

Does når apply to both medicinen virker and værelset er varmt, or only to the first part?

Semantically, når applies to both conditions:

The cough disappears slowly when
– the medicine works and
– the room is warm.

In Danish, the structure:

når [clause 1], og [clause 2]

is usually understood as:

når [clause 1] og [clause 2]

So the meaning is:

når medicinen virker og værelset er varmt
= when the medicine works and the room is warm.

Why do medicinen and værelset end in -en and -et?

Again, this is the Danish way of saying “the” by using suffixes:

en medicin – a medicine → medicinen – the medicine
(common gender: en / -en)
et værelse – a room → værelset – the room
(neuter gender: et / -et)

So:

når medicinen virker – when the medicine works
og værelset er varmt – and the room is warm

There is no separate word for “the”; it’s built into the ending of the noun.

Why is it værelset er varmt and not værelset er varm or værelset er varme?

værelse is a neuter noun (et værelse).
The basic adjective is varm (warm), and in neuter singular you add -t:

en varm stol – a warm chair (common gender)
et varmt værelse – a warm room (neuter)

When the adjective comes after the verb (predicative position), it still agrees with the noun’s gender/number:

Stolen er varm. – The chair is warm.
Værelset er varmt. – The room is warm.

So varmt is the correct neuter form agreeing with værelset.

varme appears in the plural or with the definite form:

de varme værelser – the warm rooms

Could I also say Når medicinen virker og værelset er varmt, forsvinder hosten langsomt? Is that still correct?

Yes, that’s perfectly correct and very natural.

Danish allows you to put the subordinate når-clause at the beginning:

Når medicinen virker og værelset er varmt, forsvinder hosten langsomt.

Then the main clause must still follow V2 word order (verb in second position), so:

forsvinder (verb) must come right after the whole når…-clause:
- [Når medicinen virker og værelset er varmt], forsvinder (V) hosten (S) langsomt.

Both orders mean the same:

Hosten forsvinder langsomt, når medicinen virker og værelset er varmt.
Når medicinen virker og værelset er varmt, forsvinder hosten langsomt.

Is there a more informal way to say Hosten forsvinder langsomt?

Yes, common colloquial alternatives include:

Hosten går langsomt væk. – The cough slowly goes away.
Hosten bliver langsomt væk. (less common, more dialectal/regional)

forsvinde is neutral and fine in both spoken and written Danish.
gå væk is more conversational; it’s good to recognize both.