Exact trig values worksheet for Precalculus

Precalculus expects exact values in radians as well as degrees, for all six functions, at negative angles, at angles past one full turn, and on the axes, where some values are undefined. The unit circle point (cos θ, sin θ) is the tool that handles all of them.

Also taught in Algebra 2, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Exact Trig Values Date Period Find each exact value or point. Find the exact sine, cosine or tangent $\sin ⁣ (- \frac{7 π}{6})$ $\cos ⁣ (- \frac{13 π}{6})$ $\tan ⁣ (- 240^{\circ})$ $\cos ⁣ (- 405^{\circ})$ $\tan ⁣ (- \frac{13 π}{4})$ $\tan 660^{\circ}$ $\tan \frac{17 π}{6}$ Find exact values at quadrantal angles, or write undefined $\cot ⁣ (- 900^{\circ})$ $\sin (- 10 π)$ $\csc \frac{5 π}{2}$ $\sec ⁣ (- 810^{\circ})$ $\tan (- 2 π)$ $\cos (- π)$ $\sec 1170^{\circ}$ Find the point on the unit circle Find $(\cos θ, \sin θ)$ for $θ = \frac{49 π}{6}$ . An angle of $\frac{29 π}{4}$ is in standard position. Where does it cross the unit circle? The terminal side of $2820^{\circ}$ meets the unit circle at which point? What point on the unit circle corresponds to an angle of $- \frac{2 π}{3}$ ? Write the exact coordinates where the terminal side of $- \frac{17 π}{4}$ crosses the unit circle. Give the coordinates of the point on the unit circle at $- \frac{103 π}{6}$ . 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 or point.

Find the exact sine, cosine or tangent
$\sin ⁣ (- \frac{7 π}{6})$
$\cos ⁣ (- \frac{13 π}{6})$
$\tan ⁣ (- 240^{\circ})$
$\cos ⁣ (- 405^{\circ})$
$\tan ⁣ (- \frac{13 π}{4})$
$\tan 660^{\circ}$
$\tan \frac{17 π}{6}$

Find exact values at quadrantal angles, or write undefined
$\cot ⁣ (- 900^{\circ})$
$\sin (- 10 π)$
$\csc \frac{5 π}{2}$
$\sec ⁣ (- 810^{\circ})$
$\tan (- 2 π)$
$\cos (- π)$
$\sec 1170^{\circ}$

Find the point on the unit circle
Find $(\cos θ, \sin θ)$ for $θ = \frac{49 π}{6}$ .
An angle of $\frac{29 π}{4}$ is in standard position. Where does it cross the unit circle?
The terminal side of $2820^{\circ}$ meets the unit circle at which point?
What point on the unit circle corresponds to an angle of $- \frac{2 π}{3}$ ?
Write the exact coordinates where the terminal side of $- \frac{17 π}{4}$ crosses the unit circle.
Give the coordinates of the point on the unit circle at $- \frac{103 π}{6}$ .



Sigma Prep · sigmaprep.io/worksheets Name Exact Trig ValuesAnswer keyVersion 2 Date Period Find each exact value or point. Find the exact sine, cosine or tangent $\sin ⁣ (- \frac{7 π}{6})$ $\frac{1}{2}$ $\cos ⁣ (- \frac{13 π}{6})$ $\frac{\sqrt{3}}{2}$ $\tan ⁣ (- 240^{\circ})$ $- \sqrt{3}$ $\cos ⁣ (- 405^{\circ})$ $\frac{\sqrt{2}}{2}$ $\tan ⁣ (- \frac{13 π}{4})$ $- 1$ $\tan 660^{\circ}$ $- \sqrt{3}$ $\tan \frac{17 π}{6}$ $- \frac{\sqrt{3}}{3}$ Find exact values at quadrantal angles, or write undefined $\cot ⁣ (- 900^{\circ})$ Undefined $\sin (- 10 π)$ $0$ $\csc \frac{5 π}{2}$ $1$ $\sec ⁣ (- 810^{\circ})$ Undefined $\tan (- 2 π)$ $0$ $\cos (- π)$ $- 1$ $\sec 1170^{\circ}$ Undefined Find the point on the unit circle Find $(\cos θ, \sin θ)$ for $θ = \frac{49 π}{6}$ . $(\frac{\sqrt{3}}{2}, \frac{1}{2})$ An angle of $\frac{29 π}{4}$ is in standard position. Where does it cross the unit circle? $(- \frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2})$ The terminal side of $2820^{\circ}$ meets the unit circle at which point? $(\frac{1}{2}, - \frac{\sqrt{3}}{2})$ What point on the unit circle corresponds to an angle of $- \frac{2 π}{3}$ ? $(- \frac{1}{2}, - \frac{\sqrt{3}}{2})$ Write the exact coordinates where the terminal side of $- \frac{17 π}{4}$ crosses the unit circle. $(\frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2})$ Give the coordinates of the point on the unit circle at $- \frac{103 π}{6}$ . $(- \frac{\sqrt{3}}{2}, \frac{1}{2})$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exact Trig ValuesAnswer keyVersion 2

Date Period

Find each exact value or point.

Find the exact sine, cosine or tangent
$\sin ⁣ (- \frac{7 π}{6})$ $\frac{1}{2}$
$\cos ⁣ (- \frac{13 π}{6})$ $\frac{\sqrt{3}}{2}$
$\tan ⁣ (- 240^{\circ})$ $- \sqrt{3}$
$\cos ⁣ (- 405^{\circ})$ $\frac{\sqrt{2}}{2}$
$\tan ⁣ (- \frac{13 π}{4})$ $- 1$
$\tan 660^{\circ}$ $- \sqrt{3}$
$\tan \frac{17 π}{6}$ $- \frac{\sqrt{3}}{3}$

Find exact values at quadrantal angles, or write undefined
$\cot ⁣ (- 900^{\circ})$ Undefined
$\sin (- 10 π)$ $0$
$\csc \frac{5 π}{2}$ $1$
$\sec ⁣ (- 810^{\circ})$ Undefined
$\tan (- 2 π)$ $0$
$\cos (- π)$ $- 1$
$\sec 1170^{\circ}$ Undefined

Find the point on the unit circle
Find $(\cos θ, \sin θ)$ for $θ = \frac{49 π}{6}$ . $(\frac{\sqrt{3}}{2}, \frac{1}{2})$
An angle of $\frac{29 π}{4}$ is in standard position. Where does it cross the unit circle? $(- \frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2})$
The terminal side of $2820^{\circ}$ meets the unit circle at which point? $(\frac{1}{2}, - \frac{\sqrt{3}}{2})$
What point on the unit circle corresponds to an angle of $- \frac{2 π}{3}$ ? $(- \frac{1}{2}, - \frac{\sqrt{3}}{2})$
Write the exact coordinates where the terminal side of $- \frac{17 π}{4}$ crosses the unit circle. $(\frac{\sqrt{2}}{2}, - \frac{\sqrt{2}}{2})$
Give the coordinates of the point on the unit circle at $- \frac{103 π}{6}$ . $(- \frac{\sqrt{3}}{2}, \frac{1}{2})$

How to do these

$\sec ⁣ (- \frac{2 π}{3})$

-2π/3 ends in Quadrant III, with reference angle π/3.
Cosine is negative there, so cos(-2π/3) = -1/2.
Secant is the reciprocal of cosine.

The answer is $- 2$ .

Where students go wrong

Writing 0 for an undefined value. tan(π/2) is sin over cos with cos equal to 0, so it is undefined, not 0; the same is true of sec(π/2) and csc π.

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

What you can put on this worksheet

Exact values of the special angles: $\cos \frac{π}{4}$ → $\frac{\sqrt{2}}{2}$
Exact cosecant, secant and cotangent: $\sec \frac{π}{3}$ → $2$
Angles on the axes, and undefined values: $\csc 180^{\circ}$ → Undefined
Coordinates on the unit circle: Give the coordinates of the point on the unit circle at $240^{\circ}$ . → $(- \frac{1}{2}, - \frac{\sqrt{3}}{2})$
Drawn angles, negative angles, more than one turn: Find the exact value:
$\csc ⁣ (- \frac{11 π}{6})$ → $2$

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.

You pick from 5: exact values of the special angles, exact cosecant, secant and cotangent, angles on the axes, and undefined values, coordinates on the unit circle and drawn angles, negative angles, more than one turn. Tick as many as you want and set how many of each, or let it spread them evenly.

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.

Exact trig values worksheet for Precalculus

Select your difficulty

Find the exact sine, cosine or tangent

Find exact values at quadrantal angles, or write undefined

Find the point on the unit circle

Find the exact sine, cosine or tangent

Find exact values at quadrantal angles, or write undefined

Find the point on the unit circle

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these exact trig values worksheets free?+

Do the exact trig values worksheets come with an answer key?+

Are these exact trig values worksheets printable?+

What grade are these exact trig values worksheets for?+

Can I get a different version of the same exact trig values worksheet?+

Is this a free alternative to Kuta Software for exact trig values?+

Can I choose how hard the exact trig values questions are?+

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What do students get wrong with exact trig values?+