Free · 25 minutes · 15 questions · no penalty

Trigonometry — quiz for the maturità.

15 questions drawn at random from a bank of 60 on trigonometry: every attempt is a different mix. Answer even if you are not sure — there is no penalty — and at the end you receive by email the correct answer to every question and your weak points by sub-topic — with an account you see them straight away on this page (the guided solution unlocks with your first lesson).

A free trigonometry quiz for students preparing for the maturità, Italy’s school-leaving exam.

Want to review the theory first? Read Trigonometry for the maturità, or watch sine and cosine move on the interactive unit circle.

Test in ItalianThe questions of this simulator are in Italian, as in the real exam.

Test prepared by Gaetano Livornese · Aerospace engineer, Politecnico di Milano · maths and physics tutor · updated 13 October 2026

Sub-topics covered by the quiz

Angles and special values
The fundamental identity and associated angles
Addition and double-angle formulas
Basic trigonometric equations
Basic trigonometric inequalities

Two worked examples from the test

Question 1 · Goniometria · Conversione gradi-radianti

A quanti radianti corrisponde un angolo di $150°$ ?

A $\frac{2 π}{3}$
B $\frac{3 π}{4}$
C $\frac{5 π}{6}$ correct answer
D $\frac{7 π}{6}$

Solution

Passo 1 — Regola di conversione. Per passare da gradi a radianti si moltiplica per $\frac{π}{180}$ :

$α_{r a d} = 150 \cdot \frac{π}{180}$

Passo 2 — Semplifico la frazione.

$\frac{150}{180} = \frac{5}{6}$

quindi

$α_{r a d} = \frac{5 π}{6}$

Risposta corretta: $\frac{5 π}{6}$ . Le altre opzioni corrispondono ad angoli diversi: $\frac{2 π}{3} = 120°$ , $\frac{3 π}{4} = 135°$ , $\frac{7 π}{6} = 210°$ .

Question 2 · Goniometria · Lunghezza di un arco

Un settore circolare ha raggio $r = 6 cm$ e angolo al centro $\frac{2 π}{3}$ radianti. Quanto misura l'arco corrispondente?

A $4 π$ cmcorrect answer
B $2 π$ cm
C $12 π$ cm
D $\frac{3}{π}$ cm

Solution

Passo 1 — Formula. La lunghezza di un arco è data da $l = r \cdot θ$ , dove $θ$ è l'angolo al centro in radianti.

Passo 2 — Sostituisco.

$l = 6 \cdot \frac{2 π}{3} = \frac{12 π}{3} = 4 π cm$

Risposta corretta: $4 π$ cm. Chi ottiene $12 π$ cm ha dimenticato di dividere per $3$ ; chi ottiene $2 π$ cm ha probabilmente usato $θ = \frac{π}{3}$ per errore.

In the online practice test you will find 13 more questions like these; the correct answer to every question arrives by email.

Prefer paper? Download the test as a PDF (15 questions, 5 pages · 85 KB, ready to print). You receive the solutions by email after taking it online.

Download the PDF

Where trigonometry shows up in the maturità

There is rarely a "trigonometry problem" as such: trigonometry appears inside the other exercises. In the second paper it arrives as a function to study (period, symmetries, maxima and minima), as an integral with a trigonometric substitution, or inside an optimisation problem where the unknown is an angle. In the short questions it shows up as a limit that uses the standard limits, or as a triangle to solve with the sine and cosine rules. That is why a gap here does not stay isolated: you pay for it in calculus.

What you really need to know by heart

Less than it seems. The special values of sine, cosine and tangent and their sign in the four quadrants; the fundamental identity; the addition formulas, from which the double-angle and half-angle formulas follow without learning them separately; and the graphs of the three functions with their period and range. The sum-to-product and Werner formulas are looked up on the formula sheet, not revised: in the real exam they decide nothing.

The mistake that costs you the grade

The first is giving a single solution to a trigonometric equation instead of the complete family, with + 2kπ or + kπ depending on the case, and then not selecting the ones that fall in the interval the question asks for. The second is getting the cosine from the sine with the fundamental identity and keeping only the positive root: the quadrant decides the sign. The third, in calculus, is working in degrees instead of radians — the standard limits and the derivatives of sine and cosine only hold in radians.

FAQ

How to read your score, in brief.

How are the quiz questions built?

15 multiple-choice questions (4 options), drawn at random from a bank of 60: each attempt picks a different combination. They cover angles and special values, identities, addition and double-angle formulas, graphs and period, trigonometric equations and inequalities (including linear and quadratic ones) and inverse functions.

Is there a penalty for wrong answers?

No: +1 point for every correct answer, 0 for a wrong or blank one. It is a revision quiz for the maturità, not an exam simulation — so it is always worth answering, even by guessing, and comparing your answer with the correct one.

What does the final score mean?

12 or more out of 15: the topic is solid. 8-11: needs consolidating, review the topics of the questions you got wrong and try again. Below 8: take your time to review, and it is better to go back to the theory before retrying the quiz.

Topic still weak?

Let’s look at your results together — the diagnostic is free — and I will tell you honestly what it takes to close the gap.

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