Precalculus exact trig values worksheet

The values worth knowing by heart. Easy stays in the first quadrant; the harder levels go all the way round, where the numbers repeat and only the signs change.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Exact Trig Values Date Period Find each exact value. $\sin \frac{5 π}{6}$ $\tan 33 0^{\circ}$ $\tan 15 0^{\circ}$ $\cos 33 0^{\circ}$ $\cos 12 0^{\circ}$ $\cos 22 5^{\circ}$ $\tan 13 5^{\circ}$ $\sin 22 5^{\circ}$ $\cos \frac{2 π}{3}$ $\sin \frac{7 π}{4}$ $\tan \frac{3 π}{4}$ $\tan 22 5^{\circ}$ $\cos 13 5^{\circ}$ $\tan \frac{5 π}{4}$ $\sin 12 0^{\circ}$ $\tan 30 0^{\circ}$ $\tan 18 0^{\circ}$ $\tan \frac{4 π}{3}$ $\tan π$ $\tan 31 5^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exact Trig Values

Date Period

Find each exact value.

$\sin \frac{5 π}{6}$
$\tan 33 0^{\circ}$
$\tan 15 0^{\circ}$
$\cos 33 0^{\circ}$
$\cos 12 0^{\circ}$
$\cos 22 5^{\circ}$
$\tan 13 5^{\circ}$
$\sin 22 5^{\circ}$
$\cos \frac{2 π}{3}$
$\sin \frac{7 π}{4}$
$\tan \frac{3 π}{4}$
$\tan 22 5^{\circ}$
$\cos 13 5^{\circ}$
$\tan \frac{5 π}{4}$
$\sin 12 0^{\circ}$
$\tan 30 0^{\circ}$
$\tan 18 0^{\circ}$
$\tan \frac{4 π}{3}$
$\tan π$
$\tan 31 5^{\circ}$



Sigma Prep · sigmaprep.io/worksheets Name Exact Trig ValuesAnswer keyVersion 1 Date Period Find each exact value. $\sin \frac{5 π}{6}$ $\frac{1}{2}$ $\tan 33 0^{\circ}$ $- \frac{\sqrt{3}}{3}$ $\tan 15 0^{\circ}$ $- \frac{\sqrt{3}}{3}$ $\cos 33 0^{\circ}$ $\frac{\sqrt{3}}{2}$ $\cos 12 0^{\circ}$ $- \frac{1}{2}$ $\cos 22 5^{\circ}$ $- \frac{\sqrt{2}}{2}$ $\tan 13 5^{\circ}$ $- 1$ $\sin 22 5^{\circ}$ $- \frac{\sqrt{2}}{2}$ $\cos \frac{2 π}{3}$ $- \frac{1}{2}$ $\sin \frac{7 π}{4}$ $- \frac{\sqrt{2}}{2}$ $\tan \frac{3 π}{4}$ $- 1$ $\tan 22 5^{\circ}$ $1$ $\cos 13 5^{\circ}$ $- \frac{\sqrt{2}}{2}$ $\tan \frac{5 π}{4}$ $1$ $\sin 12 0^{\circ}$ $\frac{\sqrt{3}}{2}$ $\tan 30 0^{\circ}$ $- \sqrt{3}$ $\tan 18 0^{\circ}$ $0$ $\tan \frac{4 π}{3}$ $\sqrt{3}$ $\tan π$ $0$ $\tan 31 5^{\circ}$ $- 1$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exact Trig ValuesAnswer keyVersion 1

Date Period

Find each exact value.

$\sin \frac{5 π}{6}$ $\frac{1}{2}$
$\tan 33 0^{\circ}$ $- \frac{\sqrt{3}}{3}$
$\tan 15 0^{\circ}$ $- \frac{\sqrt{3}}{3}$
$\cos 33 0^{\circ}$ $\frac{\sqrt{3}}{2}$
$\cos 12 0^{\circ}$ $- \frac{1}{2}$
$\cos 22 5^{\circ}$ $- \frac{\sqrt{2}}{2}$
$\tan 13 5^{\circ}$ $- 1$
$\sin 22 5^{\circ}$ $- \frac{\sqrt{2}}{2}$
$\cos \frac{2 π}{3}$ $- \frac{1}{2}$
$\sin \frac{7 π}{4}$ $- \frac{\sqrt{2}}{2}$
$\tan \frac{3 π}{4}$ $- 1$
$\tan 22 5^{\circ}$ $1$
$\cos 13 5^{\circ}$ $- \frac{\sqrt{2}}{2}$
$\tan \frac{5 π}{4}$ $1$
$\sin 12 0^{\circ}$ $\frac{\sqrt{3}}{2}$
$\tan 30 0^{\circ}$ $- \sqrt{3}$
$\tan 18 0^{\circ}$ $0$
$\tan \frac{4 π}{3}$ $\sqrt{3}$
$\tan π$ $0$
$\tan 31 5^{\circ}$ $- 1$

How to do these

$\sin 21 0^{\circ}$

210 is in the third quadrant, where sine is negative.
Its reference angle is 30.
Sine of 30 is one half.

The answer is $- \frac{1}{2}$ .

Where students go wrong

Getting the sign right and the number wrong, or the other way round. Do them separately: the reference angle gives the number, the quadrant gives the sign.

Also called unit circle values, special angles or trig values without a calculator.

Questions about these worksheets

Yes. Every exact trig values sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the exact trig values questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Getting the sign right and the number wrong, or the other way round. Do them separately: the reference angle gives the number, the quadrant gives the sign.

Precalculus exact trig values worksheet

Select your difficulty

Exact Trig Values

Exact Trig ValuesAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

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