State the domain and range: y = 2tan ^-1(x + 3)

Domain (-infinity, infinity), range (-π, π)

Give the domain and range: y = cos ^-1(x) - 2

Domain [-1, 1]; range [-2, -2 + π]

Give the domain and range: y = sec ^-1(x - 4)

Domain (-infinity, 3] or [5, infinity); range [0, π/2) or (π/2, π]

Graph y = cos ^-1(x) + 1 and give its domain and range.

Domain [-1, 1]; range [1, 1 + π]

Give the domain and range of y = sin ^-1(sin x), and sketch it.

Domain (-infinity, infinity); range [-π/2, π/2]; a zigzag of slope 1 and -1

Worksheets · Precalculus

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.

Select your difficulty

Pick more than one for a sheet that mixes them.

Question order

Difficulty

Printing options

Working space

Answer key

Print an answer key on a second page

Version

On the answer key. Type it in to get that sheet back.

Download PDF Print instead

Free, no account. Make as many different versions as you need.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Inverse Trig Functions Date Period Answer each question. Give exact values. Find exact values of inverse trig functions Find the exact value, in radians: $\sin^{- 1} ⁣ (\frac{1}{2})$ Find the exact value: $\cos ⁣ (\sin^{- 1} ⁣ (\frac{3}{5}))$ Find the exact value, in radians: $\cos^{- 1} ⁣ (- \frac{\sqrt{3}}{2})$ Find the exact value: $\sin ⁣ (\cos^{- 1} ⁣ (\frac{8}{17}))$ Find exact values outside the principal range Find the exact value: $\tan^{- 1} ⁣ (\tan ⁣ (- \frac{2 π}{3}))$ Find the exact value: $\tan^{- 1} (\tan (- π))$ Find the exact value: $\sin^{- 1} ⁣ (\sin ⁣ (- \frac{3 π}{2}))$ Find the exact value: $\cos^{- 1} ⁣ (\cos ⁣ (\frac{8 π}{3}))$ Write a composition as an algebraic expression Write as an algebraic expression in $x$ : $\cot ⁣ (\sin^{- 1} ⁣ (\frac{x}{5}))$ Write as an algebraic expression in $x$ : $\sin ⁣ (\cos^{- 1} x)$ Write as an algebraic expression in $x$ : $\sec ⁣ (\sin^{- 1} x)$ Evaluate $\sec^{-1}$ , $\csc^{-1}$ and $\cot^{-1}$ Find the exact value: $\csc^{- 1} ⁣ (\sqrt{2})$ Find the exact value: $\cot^{- 1} (- 1)$ (range $(0, π)$ ) Find the exact value: $\sec^{- 1} (- 1)$ Find exact values of compositions Find the exact value: $\cos ⁣ (\sin^{- 1} ⁣ (- \frac{5}{13}))$ Find the exact value: $\tan ⁣ (\cos^{- 1} ⁣ (\frac{3}{5}))$ Find the exact value: $\tan ⁣ (\sin^{- 1} ⁣ (- \frac{3}{5}))$ State the domain and range State the domain and range: $y = \cos^{- 1} (x + 4)$ State the domain and range: $y = 2 \tan^{- 1} (x + 3)$ State the domain and range: $y = 2 \cos^{- 1} (x + 1)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse Trig Functions

Date Period

Answer each question. Give exact values.

Find exact values of inverse trig functions
Find the exact value, in radians:
$\sin^{- 1} ⁣ (\frac{1}{2})$
Find the exact value:
$\cos ⁣ (\sin^{- 1} ⁣ (\frac{3}{5}))$
Find the exact value, in radians:
$\cos^{- 1} ⁣ (- \frac{\sqrt{3}}{2})$
Find the exact value:
$\sin ⁣ (\cos^{- 1} ⁣ (\frac{8}{17}))$

Find exact values outside the principal range
Find the exact value:
$\tan^{- 1} ⁣ (\tan ⁣ (- \frac{2 π}{3}))$
Find the exact value: $\tan^{- 1} (\tan (- π))$
Find the exact value:
$\sin^{- 1} ⁣ (\sin ⁣ (- \frac{3 π}{2}))$
Find the exact value:
$\cos^{- 1} ⁣ (\cos ⁣ (\frac{8 π}{3}))$

Write a composition as an algebraic expression
Write as an algebraic expression in $x$ : $\cot ⁣ (\sin^{- 1} ⁣ (\frac{x}{5}))$
Write as an algebraic expression in $x$ : $\sin ⁣ (\cos^{- 1} x)$
Write as an algebraic expression in $x$ : $\sec ⁣ (\sin^{- 1} x)$

Evaluate $\sec^{-1}$ , $\csc^{-1}$ and $\cot^{-1}$
Find the exact value: $\csc^{- 1} ⁣ (\sqrt{2})$
Find the exact value: $\cot^{- 1} (- 1)$ (range $(0, π)$ )
Find the exact value: $\sec^{- 1} (- 1)$

Find exact values of compositions
Find the exact value:
$\cos ⁣ (\sin^{- 1} ⁣ (- \frac{5}{13}))$
Find the exact value:
$\tan ⁣ (\cos^{- 1} ⁣ (\frac{3}{5}))$
Find the exact value:
$\tan ⁣ (\sin^{- 1} ⁣ (- \frac{3}{5}))$

State the domain and range
State the domain and range: $y = \cos^{- 1} (x + 4)$
State the domain and range: $y = 2 \tan^{- 1} (x + 3)$
State the domain and range: $y = 2 \cos^{- 1} (x + 1)$



Sigma Prep · sigmaprep.io/worksheets Name Inverse Trig FunctionsAnswer keyVersion 1 Date Period Answer each question. Give exact values. Find exact values of inverse trig functions Find the exact value, in radians: $\sin^{- 1} ⁣ (\frac{1}{2})$ $\frac{π}{6}$ Find the exact value: $\cos ⁣ (\sin^{- 1} ⁣ (\frac{3}{5}))$ $\frac{4}{5}$ Find the exact value, in radians: $\cos^{- 1} ⁣ (- \frac{\sqrt{3}}{2})$ $\frac{5 π}{6}$ Find the exact value: $\sin ⁣ (\cos^{- 1} ⁣ (\frac{8}{17}))$ $\frac{15}{17}$ Find exact values outside the principal range Find the exact value: $\tan^{- 1} ⁣ (\tan ⁣ (- \frac{2 π}{3}))$ $\frac{π}{3}$ Find the exact value: $\tan^{- 1} (\tan (- π))$ $0$ Find the exact value: $\sin^{- 1} ⁣ (\sin ⁣ (- \frac{3 π}{2}))$ $\frac{π}{2}$ Find the exact value: $\cos^{- 1} ⁣ (\cos ⁣ (\frac{8 π}{3}))$ $\frac{2 π}{3}$ Write a composition as an algebraic expression Write as an algebraic expression in $x$ : $\cot ⁣ (\sin^{- 1} ⁣ (\frac{x}{5}))$ $\frac{\sqrt{25 - x^{2}}}{x}$ Write as an algebraic expression in $x$ : $\sin ⁣ (\cos^{- 1} x)$ $\sqrt{1 - x^{2}}$ Write as an algebraic expression in $x$ : $\sec ⁣ (\sin^{- 1} x)$ $\frac{1}{\sqrt{1 - x^{2}}}$ Evaluate $\sec^{-1}$ , $\csc^{-1}$ and $\cot^{-1}$ Find the exact value: $\csc^{- 1} ⁣ (\sqrt{2})$ $\frac{π}{4}$ Find the exact value: $\cot^{- 1} (- 1)$ (range $(0, π)$ ) $\frac{3 π}{4}$ Find the exact value: $\sec^{- 1} (- 1)$ $π$ Find exact values of compositions Find the exact value: $\cos ⁣ (\sin^{- 1} ⁣ (- \frac{5}{13}))$ $\frac{12}{13}$ Find the exact value: $\tan ⁣ (\cos^{- 1} ⁣ (\frac{3}{5}))$ $\frac{4}{3}$ Find the exact value: $\tan ⁣ (\sin^{- 1} ⁣ (- \frac{3}{5}))$ $- \frac{3}{4}$ State the domain and range State the domain and range: $y = \cos^{- 1} (x + 4)$ Domain $[- 5, - 3]$ , range $[0, π]$ State the domain and range: $y = 2 \tan^{- 1} (x + 3)$ Domain $(- \infty, \infty)$ , range $(- π, π)$ State the domain and range: $y = 2 \cos^{- 1} (x + 1)$ Domain $[- 2, 0]$ , range $[0, 2 π]$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Inverse Trig FunctionsAnswer keyVersion 1

Date Period

Answer each question. Give exact values.

Find exact values of inverse trig functions
Find the exact value, in radians:
$\sin^{- 1} ⁣ (\frac{1}{2})$ $\frac{π}{6}$
Find the exact value:
$\cos ⁣ (\sin^{- 1} ⁣ (\frac{3}{5}))$ $\frac{4}{5}$
Find the exact value, in radians:
$\cos^{- 1} ⁣ (- \frac{\sqrt{3}}{2})$ $\frac{5 π}{6}$
Find the exact value:
$\sin ⁣ (\cos^{- 1} ⁣ (\frac{8}{17}))$ $\frac{15}{17}$

Find exact values outside the principal range
Find the exact value:
$\tan^{- 1} ⁣ (\tan ⁣ (- \frac{2 π}{3}))$ $\frac{π}{3}$
Find the exact value: $\tan^{- 1} (\tan (- π))$ $0$
Find the exact value:
$\sin^{- 1} ⁣ (\sin ⁣ (- \frac{3 π}{2}))$ $\frac{π}{2}$
Find the exact value:
$\cos^{- 1} ⁣ (\cos ⁣ (\frac{8 π}{3}))$ $\frac{2 π}{3}$

Write a composition as an algebraic expression
Write as an algebraic expression in $x$ : $\cot ⁣ (\sin^{- 1} ⁣ (\frac{x}{5}))$ $\frac{\sqrt{25 - x^{2}}}{x}$
Write as an algebraic expression in $x$ : $\sin ⁣ (\cos^{- 1} x)$ $\sqrt{1 - x^{2}}$
Write as an algebraic expression in $x$ : $\sec ⁣ (\sin^{- 1} x)$ $\frac{1}{\sqrt{1 - x^{2}}}$

Evaluate $\sec^{-1}$ , $\csc^{-1}$ and $\cot^{-1}$
Find the exact value: $\csc^{- 1} ⁣ (\sqrt{2})$ $\frac{π}{4}$
Find the exact value: $\cot^{- 1} (- 1)$ (range $(0, π)$ ) $\frac{3 π}{4}$
Find the exact value: $\sec^{- 1} (- 1)$ $π$

Find exact values of compositions
Find the exact value:
$\cos ⁣ (\sin^{- 1} ⁣ (- \frac{5}{13}))$ $\frac{12}{13}$
Find the exact value:
$\tan ⁣ (\cos^{- 1} ⁣ (\frac{3}{5}))$ $\frac{4}{3}$
Find the exact value:
$\tan ⁣ (\sin^{- 1} ⁣ (- \frac{3}{5}))$ $- \frac{3}{4}$

State the domain and range
State the domain and range: $y = \cos^{- 1} (x + 4)$ Domain $[- 5, - 3]$ , range $[0, π]$
State the domain and range: $y = 2 \tan^{- 1} (x + 3)$ Domain $(- \infty, \infty)$ , range $(- π, π)$
State the domain and range: $y = 2 \cos^{- 1} (x + 1)$ Domain $[- 2, 0]$ , range $[0, 2 π]$

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.

What you can put on this worksheet

Exact values of inverse functions: Find the exact value, in degrees:
$\cos^{- 1} ⁣ (- \frac{\sqrt{2}}{2})$ → $135^{\circ}$
Angles outside the principal range: Find the exact value:
$\cos^{- 1} ⁣ (\cos ⁣ (\frac{5 π}{4}))$ → $\frac{3 π}{4}$
A composition as an algebraic expression: Write as an algebraic expression in $x$ : $\sec ⁣ (\sin^{- 1} x)$ → $\frac{1}{\sqrt{1 - x^{2}}}$
Inverse secant, cosecant and cotangent: Find the exact value:
$\csc^{- 1} ⁣ (\frac{2 \sqrt{3}}{3})$ → $\frac{π}{3}$
Compositions with negative values: Find the exact value:
$\tan ⁣ (\cos^{- 1} ⁣ (- \frac{8}{17}))$ → $- \frac{15}{8}$
Domain and range: State the domain and range: $y = 2 \cos^{- 1} (x)$ → Domain $[- 1, 1]$ , range $[0, 2 π]$
Domain and range with a stretch or shift: Give the domain and range: $y = \cos^{- 1} (x) - 2$ → Domain $[- 1, 1]$ ; range $[- 2, - 2 + π]$
Domain and range of shifted csc^-1, sec^-1, cot^-1: Give the domain and range: $y = \sec^{- 1} (x - 4)$ → Domain $(- \infty, 3] \cup [5, \infty)$ ; range $[0, \frac{π}{2}) \cup (\frac{π}{2}, π]$
A trig function of csc^-1 or sec^-1: $\cos ⁣ (\csc^{- 1} \frac{17}{8})$ → $\frac{15}{17}$
An inverse of a different function: $\tan^{- 1} ⁣ (\cot \frac{π}{6})$ → $\frac{π}{3}$
More algebraic expressions: Write as an algebraic expression in $x$ : $\sin ⁣ (\sec^{- 1} \frac{x}{3})$ → $\frac{\sqrt{x^{2} - 9}}{∣ x ∣}$
Graph a moved inverse function: Graph $y = \cos^{- 1} (x) + 1$ and give its domain and range. → Domain $[- 1, 1]$ ; range $[1, 1 + π]$
Composites: domain, range, sketch: Give the domain and range of $y = \sin^{- 1} (\sin x)$ , and sketch it. → Domain $(- \infty, \infty)$ ; range $[- \frac{π}{2}, \frac{π}{2}]$ ; a zigzag of slope 1 and −1

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 three 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 13: exact values of inverse functions, angles outside the principal range, a composition as an algebraic expression, inverse secant, cosecant and cotangent, compositions with negative values, domain and range, domain and range with a stretch or shift, domain and range of shifted csc^-1, sec^-1, cot^-1, a trig function of csc^-1 or sec^-1, an inverse of a different function, more algebraic expressions, graph a moved inverse function and composites: domain, range, sketch. Tick as many as you want and set how many of each, or let it spread them evenly.

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

Find exact values of inverse trig functions

Find exact values outside the principal range

Write a composition as an algebraic expression

Evaluate sec⁡−1\sec^{-1}sec−1, csc⁡−1\csc^{-1}csc−1 and cot⁡−1\cot^{-1}cot−1

Find exact values of compositions

State the domain and range

Find exact values of inverse trig functions

Find exact values outside the principal range

Write a composition as an algebraic expression

Evaluate sec⁡−1\sec^{-1}sec−1, csc⁡−1\csc^{-1}csc−1 and cot⁡−1\cot^{-1}cot−1

Find exact values of compositions

State the domain and range

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these inverse trig functions worksheets free?+

Do the inverse trig functions worksheets come with an answer key?+

Are these inverse trig functions worksheets printable?+

What grade are these inverse trig functions worksheets for?+

Can I get a different version of the same inverse trig functions worksheet?+

Is this a free alternative to Kuta Software for inverse trig functions?+

Can I choose how hard the inverse trig functions questions are?+

What kinds of question are on a inverse trig functions worksheet?+

What do students get wrong with inverse trig functions?+

Evaluate $\sec^{-1}$ , $\csc^{-1}$ and $\cot^{-1}$

Evaluate $\sec^{-1}$ , $\csc^{-1}$ and $\cot^{-1}$