Inverse trig functions worksheet

An inverse trig function answers "which angle?" and it is only allowed to give one. That restriction is the whole difficulty: the answer has to be in the range that function is allowed to use.

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Sigma Prep · sigmaprep.io/worksheets Name Inverse Trig Functions Date Period Evaluate each expression exactly. $\sin^{- 1} 0$ , in radians $\tan^{- 1} - 1$ , in radians $\tan^{- 1} - \frac{\sqrt{3}}{3}$ , in radians $\cos^{- 1} 0$ , in radians $\sin (\sin^{- 1} \frac{5}{13})$ $\tan (\sin^{- 1} - \frac{5}{13})$ $\cos (\cos^{- 1} \frac{5}{13})$ $\cos (\cos^{- 1} \frac{3}{5})$ $\sin^{- 1} \frac{\sqrt{2}}{2}$ , in radians $\tan^{- 1} \sqrt{3}$ , in radians $\sin (\sin^{- 1} \frac{7}{25})$ $\tan (\cos^{- 1} \frac{3}{5})$ $\sin (\cos^{- 1} \frac{5}{13})$ $\sin^{- 1} 1$ , in radians $\cos^{- 1} \frac{\sqrt{2}}{2}$ , in radians $\tan^{- 1} 1$ , in radians $\sin^{- 1} - 1$ , in radians $\sin^{- 1} \frac{\sqrt{3}}{2}$ , in radians $\tan^{- 1} \frac{\sqrt{3}}{3}$ , in radians $\tan (\sin^{- 1} \frac{8}{17})$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse Trig Functions

Date Period

Evaluate each expression exactly.

$\sin^{- 1} 0$ , in radians
$\tan^{- 1} - 1$ , in radians
$\tan^{- 1} - \frac{\sqrt{3}}{3}$ , in radians
$\cos^{- 1} 0$ , in radians
$\sin (\sin^{- 1} \frac{5}{13})$
$\tan (\sin^{- 1} - \frac{5}{13})$
$\cos (\cos^{- 1} \frac{5}{13})$
$\cos (\cos^{- 1} \frac{3}{5})$
$\sin^{- 1} \frac{\sqrt{2}}{2}$ , in radians
$\tan^{- 1} \sqrt{3}$ , in radians
$\sin (\sin^{- 1} \frac{7}{25})$
$\tan (\cos^{- 1} \frac{3}{5})$
$\sin (\cos^{- 1} \frac{5}{13})$
$\sin^{- 1} 1$ , in radians
$\cos^{- 1} \frac{\sqrt{2}}{2}$ , in radians
$\tan^{- 1} 1$ , in radians
$\sin^{- 1} - 1$ , in radians
$\sin^{- 1} \frac{\sqrt{3}}{2}$ , in radians
$\tan^{- 1} \frac{\sqrt{3}}{3}$ , in radians
$\tan (\sin^{- 1} \frac{8}{17})$



Sigma Prep · sigmaprep.io/worksheets Name Inverse Trig FunctionsAnswer keyVersion 1 Date Period Evaluate each expression exactly. $\sin^{- 1} 0$ , in radians $0$ $\tan^{- 1} - 1$ , in radians $- \frac{π}{4}$ $\tan^{- 1} - \frac{\sqrt{3}}{3}$ , in radians $- \frac{π}{6}$ $\cos^{- 1} 0$ , in radians $\frac{π}{2}$ $\sin (\sin^{- 1} \frac{5}{13})$ $\frac{5}{13}$ $\tan (\sin^{- 1} - \frac{5}{13})$ $- \frac{5}{12}$ $\cos (\cos^{- 1} \frac{5}{13})$ $\frac{5}{13}$ $\cos (\cos^{- 1} \frac{3}{5})$ $\frac{3}{5}$ $\sin^{- 1} \frac{\sqrt{2}}{2}$ , in radians $\frac{π}{4}$ $\tan^{- 1} \sqrt{3}$ , in radians $\frac{π}{3}$ $\sin (\sin^{- 1} \frac{7}{25})$ $\frac{7}{25}$ $\tan (\cos^{- 1} \frac{3}{5})$ $\frac{4}{3}$ $\sin (\cos^{- 1} \frac{5}{13})$ $\frac{12}{13}$ $\sin^{- 1} 1$ , in radians $\frac{π}{2}$ $\cos^{- 1} \frac{\sqrt{2}}{2}$ , in radians $\frac{π}{4}$ $\tan^{- 1} 1$ , in radians $\frac{π}{4}$ $\sin^{- 1} - 1$ , in radians $- \frac{π}{2}$ $\sin^{- 1} \frac{\sqrt{3}}{2}$ , in radians $\frac{π}{3}$ $\tan^{- 1} \frac{\sqrt{3}}{3}$ , in radians $\frac{π}{6}$ $\tan (\sin^{- 1} \frac{8}{17})$ $\frac{8}{15}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse Trig FunctionsAnswer keyVersion 1

Date Period

Evaluate each expression exactly.

$\sin^{- 1} 0$ , in radians $0$
$\tan^{- 1} - 1$ , in radians $- \frac{π}{4}$
$\tan^{- 1} - \frac{\sqrt{3}}{3}$ , in radians $- \frac{π}{6}$
$\cos^{- 1} 0$ , in radians $\frac{π}{2}$
$\sin (\sin^{- 1} \frac{5}{13})$ $\frac{5}{13}$
$\tan (\sin^{- 1} - \frac{5}{13})$ $- \frac{5}{12}$
$\cos (\cos^{- 1} \frac{5}{13})$ $\frac{5}{13}$
$\cos (\cos^{- 1} \frac{3}{5})$ $\frac{3}{5}$
$\sin^{- 1} \frac{\sqrt{2}}{2}$ , in radians $\frac{π}{4}$
$\tan^{- 1} \sqrt{3}$ , in radians $\frac{π}{3}$
$\sin (\sin^{- 1} \frac{7}{25})$ $\frac{7}{25}$
$\tan (\cos^{- 1} \frac{3}{5})$ $\frac{4}{3}$
$\sin (\cos^{- 1} \frac{5}{13})$ $\frac{12}{13}$
$\sin^{- 1} 1$ , in radians $\frac{π}{2}$
$\cos^{- 1} \frac{\sqrt{2}}{2}$ , in radians $\frac{π}{4}$
$\tan^{- 1} 1$ , in radians $\frac{π}{4}$
$\sin^{- 1} - 1$ , in radians $- \frac{π}{2}$
$\sin^{- 1} \frac{\sqrt{3}}{2}$ , in radians $\frac{π}{3}$
$\tan^{- 1} \frac{\sqrt{3}}{3}$ , in radians $\frac{π}{6}$
$\tan (\sin^{- 1} \frac{8}{17})$ $\frac{8}{15}$

How to do these

$\cos^{- 1} (- \frac{1}{2})$

Cosine is one half at pi over 3.
Inverse cosine answers between 0 and pi.
The one in that range is 2 pi over 3.

The answer is $\frac{2 π}{3}$ .

Where students go wrong

Giving every angle with the right ratio. An inverse function has one output, so arcsin lives between minus pi over 2 and pi over 2, and arccos between 0 and pi. Anything outside is not the answer.

Also called arcsin arccos arctan, evaluating inverse trig or inverse sine cosine tangent.

Questions about these worksheets

Yes. Every inverse trig functions 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 inverse trig functions 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.

Giving every angle with the right ratio. An inverse function has one output, so arcsin lives between minus pi over 2 and pi over 2, and arccos between 0 and pi. Anything outside is not the answer.

Inverse trig functions worksheet

Select your difficulty

Inverse Trig Functions

Inverse Trig FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

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