die Trainerin
coach
A woman who guides and trains a person or a team in the field of sports.
Die neue Trainerin hat die Motivation des Volleyballteams deutlich gesteigert.
The new coach significantly increased the volleyball team's motivation.

female trainer
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coach
A woman who guides and trains a person or a team in the field of sports.
Die neue Trainerin hat die Motivation des Volleyballteams deutlich gesteigert.
The new coach significantly increased the volleyball team's motivation.

'Trainerin' (female trainer/coach) is the feminine form of 'der Trainer' (the male trainer/coach). In German, the ending '-in' is commonly added to many masculine job titles and personal nouns to form the feminine form.
Sie arbeitet als persönliche Trainerin in einem Fitnessstudio.
She works as a personal trainer in a gym.
To describe a trainer's specialization, you use 'für' + accusative, e.g. 'Trainerin für Kommunikation' (communication trainer). To name the team or person being trained, you use 'von' + dative, e.g. 'Trainerin von der Jugendmannschaft' (coach of the youth team).
Sie ist die neue Trainerin von unserem Team.
She is the new coach of our team.
You can tell from the context whether a sports coach or a seminar trainer is meant. Words like 'Mannschaft' (team), 'Team' (team), or a type of sport point to sports. Words like 'Seminar' (seminar), 'Kurs' (course), or 'Firma' (company) point to professional training.
Die Handball-Trainerin bespricht die Taktik für das nächste Spiel.
The handball coach discusses the tactics for the next game.
To specify the type of training, 'Trainerin' (female trainer/coach) is often used as the second part of a compound noun. Examples are 'Fitnesstrainerin' (female fitness trainer), 'Yogalehrerin' (female yoga teacher), or 'Kommunikationstrainerin' (female communication trainer).
Meine Fitnesstrainerin erstellt mir jede Woche einen neuen Plan.
My fitness trainer creates a new plan for me every week.
trainer / coach
'der Trainer' and 'die Trainerin' both refer to a person who guides others in sports or in a course. The difference is the person's gender and the article. 'der Trainer' is used for a man, or sometimes generally when gender is not important. 'die Trainerin' is used for a woman. Learners may confuse the words because the role can be the same: both can train a team or lead a seminar. So pay attention above all to the person and the correct article.

Die Trainerin zeigt den Teilnehmern im Seminar praktische Übungen.
The trainer shows the participants practical exercises in the seminar.
Der Trainer erklärt der Mannschaft vor dem Spiel die neue Taktik.
Before the game, the coach explains the new tactic to the team.