What does this Trigonometry cheat sheet cover?

It has 9 sections: Angles & Circle, Right Triangle, Core Identities, Angle Formulas, Double & Half, Laws, Graphs, Inverse Trig and Solve Equations. Together they cover the topics a typical Trigonometry exam tests, including unit circle values, right-triangle definitions, reciprocal and quotient identities and Pythagorean identities.

Is the trig identities cheat sheet free?

The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.

Can I bring this Trigonometry cheat sheet to my exam?

Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.

The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it made no corrections before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.

Can I make a Trigonometry sheet from my own notes?

Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

MathTrigonometry

Trig Identities Cheat Sheet — 1-page PDF

Unit circle, identities, equations, laws, and trig graphs. The whole course on one dense, printable page for your midterm or final, with every formula typeset and worked examples where they help.

Make this from your notes Unlock the full sheet

The first part is free below. See pricing →

For a specific exam: Trigonometry Final exam study sheet.

1 pageUS Letter
9 sections10 topics
Free previewfull sheet with Unlimited

Preview of the one-page Trigonometry cheat sheet: Unit circle, identities, equations, laws, and trig graphs — the whole course, one page

On the sheet

What’s on it

The topics a typical Trigonometry exam tests, all on the one page.

Unit circle values
Right-triangle definitions
Reciprocal and quotient identities
Pythagorean identities
Sum and difference formulas
Double and half angle formulas
Law of sines and cosines
Graphs: amplitude, period, phase shift
Inverse trig ranges
Solving trig equations

Free preview

The free part, as text

The free part of the sheet, section by section. Unlock the full sheet to read the rest, edit any block, and print it or save it as a PDF.

01Angles & Circle

Radian: Angle measure $θ$ with $θ = s / r$ on a circle of radius $r$ ; full turn $= 2 π$ rad.

Degree-radian

deg	rad
$0$	$0$
$30$	$π /6$
$45$	$π /4$
$60$	$π /3$
$90$	$π /2$
$180$	$π$
$270$	$3 π /2$
$360$	$2 π$

Unit circle: Circle $x^{2} + y^{2} = 1$ . For angle $θ$ , point $P = (cos θ, sin θ)$ .

Trig on unit circle

cos θ = x, sin θ = y, tan θ = \frac{y}{x} = \frac{s i n θ}{c o s θ}

$x \neq = 0$ for $tan θ$ .

Quadrantal values

$θ$	$sin θ$	$cos θ$	$tan θ$
$0$	$0$	$1$	$0$
$π /2$	$1$	$0$	undef
$π$	$0$	$- 1$	$0$
$3 π /2$	$- 1$	$0$	undef

02Right Triangle

Watch out:For obtuse/negative angles, right-triangle definitions do not apply directly; use the unit circle.

03Core Identities

Reciprocal

sin θ csc θ = 1, cos θ sec θ = 1, tan θ cot θ = 1

Pythagorean

sin^{2} θ + cos^{2} θ = 1

From $x^{2} + y^{2} = 1$ on unit circle.

Pythagorean 2

1 + tan^{2} θ = sec^{2} θ

Divide $sin^{2} + cos^{2} = 1$ by $cos^{2} θ$ .

Pythagorean 3

1 + cot^{2} θ = csc^{2} θ

Divide by $sin^{2} θ$ .

Even/odd

sin (- θ) = - sin θ, cos (- θ) = cos θ, tan (- θ) = - tan θ

Also $csc, cot$ odd; $sec$ even.

Ex.Given $sin θ = 3/5$ and $θ$ in QI, find $cos θ$ and $tan θ$ .

$cos θ = 1 - 9/25 = 4/5$ . Then $tan θ = (3/5) / (4/5) = 3/4$ .

04Double & Half

Ex.Find $cos 2 θ$ if $sin θ = 5/13$ and $θ$ in QI.

$cos θ = 12/13$ . Then $cos 2 θ = (12/13)^{2} - (5/13)^{2} = 119/169$ .

05Laws

Law of sines

\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}

In any triangle $A B C$ with opposite sides $a, b, c$ .

Area

K = \frac{1}{2} ab sin C = \frac{1}{2} b c sin A = \frac{1}{2} c a sin B

Triangle area.

Law of cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Cyclic permutations for $a, b$ .

Cosine form

cos C = \frac{a ^{2} + b ^{2} - c ^{2}}{2 ab}

Solve for included angle.

Use when

given	best law
ASA/AAS	law of sines
SAS/SSS	law of cosines
area with two sides+included angle	$K = \frac{1}{2} ab sin C$

06Inverse Trig

Domains

function	domain
$arcsin x$	$[- 1, 1]$
$arccos x$	$[- 1, 1]$
$arctan x$	$R$

Composition

sin (arcsin x) = x, cos (arccos x) = x, tan (arctan x) = x

For inputs in the domain.

Ex.Evaluate $arccos (- 1)$ and $arcsin (1/2)$ .

$arccos (- 1) = π$ . $arcsin (1/2) = π /6$ .

07Solve Equations

Isolate one trig function.
Use unit circle / inverse trig to get reference angles.
Apply periodicity: $sin, cos$ period $2 π$ ; $tan$ period $π$ .
Restrict to the required interval.
Check extraneous solutions if equation was transformed.

Sine solutions

sin x = sin α \Rightarrow x = α + 2 k π or x = π - α + 2 k π

All integers $k$ .

Cheat sheet locked

Also on the full Trigonometry sheet

8 more sections, with every definition, formula and worked example. Unlimited unlocks every full sheet in the library to edit, print or save as a PDF, and makes unlimited sheets from your own notes.

Angles & Circle

Special-angle values

Right Triangle

Right-triangle ratios
Reciprocals
Quotients
Domain notes

Angle Formulas

Sum
Cos sum
Tan sum
Difference

Double & Half

Double-angle
Half-angle
Half-angle tan

Laws

Graphs

General sine
General cosine
General tangent
Graph features

Inverse Trig

Principal values
Ranges

Solve Equations

Cosine solutions
Tangent solutions

Unlock the full sheet $4.99 a month or $19 a semester

Or make this from your own notes

FAQ

Questions

About the Trigonometry sheet and making your own.

What does this Trigonometry cheat sheet cover?: It has 9 sections: Angles & Circle, Right Triangle, Core Identities, Angle Formulas, Double & Half, Laws, Graphs, Inverse Trig and Solve Equations. Together they cover the topics a typical Trigonometry exam tests, including unit circle values, right-triangle definitions, reciprocal and quotient identities and Pythagorean identities.
Is the trig identities cheat sheet free?: The first part is free to read on this page, with no account needed. The full sheet opens in the app with Unlimited ($4.99 a month or $19 for a semester), where you can edit it, print it or save it as a PDF. It is one US Letter page and prints cleanly in black and white or colour.
Can I bring this Trigonometry cheat sheet to my exam?: Only if your course allows a note sheet, so check the syllabus. This one is a single US Letter page. If your exam allows a different size, such as a 3x5 or 4x6 index card or one page front and back, Cheat Sheet AI makes one at exactly that size from your own lecture notes.
How accurate is it?: The sheet was written by our engine from a standard course outline, then a second model fact-checked every formula and statement against it; it made no corrections before publishing. Notation and emphasis vary between courses, so check it against your own lecture notes.
Can I make a Trigonometry sheet from my own notes?: Yes. Upload your lecture slides, notes or study guide and Cheat Sheet AI writes a sheet in your course's notation, sized to exactly the space your exam allows. Your first sheets are free.

Keep going

All 40 sheets are in the sheet library.

Your course, your notes, one page.

Make this from your notes

Upload your own Trigonometry slides or notes and get a study sheet in your course’s notation. Your first sheet needs no account, and a free account adds one more. See pricing