Find all solutions: 3cos x = cos x + sqrt(2)

x = π/4 + 2π k, 7π/4 + 2π k

Find all solutions: 5cos x - sqrt(3) = 3cos x

x = π/6 + 2π k, 11π/6 + 2π k

Solve on [0, 2π): tan 3x = 0

0, π/3, 2π/3, π, 4π/3, 5π/3

Trig equations worksheet for Precalculus

The calculator gives you one angle. The rest come from knowing where else that ratio takes the same value, which is what the unit circle is for.

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

Select your difficulty

Pick more than one for a sheet that mixes them.

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



Sigma Prep · sigmaprep.io/worksheets Name Trig Equations Date Period Solve each equation on [0, 2π) unless another interval is given or it asks for all solutions. Solve basic trig equations on $[0, 2\pi)$ $2 \cos x = 2$ $2 \sin x = 2$ $\tan x = 1$ $2 \sin x = - 2$ Find all solutions Find all solutions: $2 \sin^{2} x = 1$ Find all solutions: $3 \cos x = \cos x + \sqrt{2}$ Find all solutions: $\tan^{2} x = 3$ Find all solutions: $5 \cos x - \sqrt{3} = 3 \cos x$ Solve with $\sec$ , $\csc$ and $\cot$ Solve on $[0, 2 π)$ : $5 \csc x - 2 \sqrt{3} = 2 \csc x$ Solve on $[0, 2 π)$ : $\sqrt{3} \cot x + 2 = 1$ Solve on $[0, 2 π)$ : $\sqrt{3} \sec x + 5 = 3$ Solve on $[0, 2 π)$ : $6 \sec x - 4 \sqrt{3} = - 8 \sqrt{3}$ Solve with a shifted angle Solve on $[0, 2 π)$ : $3 \tan ⁣ (x - \frac{π}{3}) = - 3$ Solve on $[0, 2 π)$ : $3 \sin ⁣ (x - \frac{π}{6}) = 3$ Solve on $[0, 2 π)$ : $2 \sin ⁣ (x - \frac{2 π}{3}) = - 2$ Solve on $[0, 2 π)$ : $2 \tan ⁣ (x - \frac{3 π}{4}) = 0$ Solve in degrees to the nearest tenth Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $8 \sin x = - 3$ Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $7 \tan x = - 14$ Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $2 \cos x = 1$ Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $9 \cos x = - 4$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Trig Equations

Date Period

Solve each equation on [0, 2π) unless another interval is given or it asks for all solutions.

Solve basic trig equations on $[0, 2\pi)$
$2 \cos x = 2$
$2 \sin x = 2$
$\tan x = 1$
$2 \sin x = - 2$

Find all solutions
Find all solutions: $2 \sin^{2} x = 1$
Find all solutions: $3 \cos x = \cos x + \sqrt{2}$
Find all solutions: $\tan^{2} x = 3$
Find all solutions: $5 \cos x - \sqrt{3} = 3 \cos x$

Solve with $\sec$ , $\csc$ and $\cot$
Solve on $[0, 2 π)$ : $5 \csc x - 2 \sqrt{3} = 2 \csc x$
Solve on $[0, 2 π)$ : $\sqrt{3} \cot x + 2 = 1$
Solve on $[0, 2 π)$ : $\sqrt{3} \sec x + 5 = 3$
Solve on $[0, 2 π)$ : $6 \sec x - 4 \sqrt{3} = - 8 \sqrt{3}$

Solve with a shifted angle
Solve on $[0, 2 π)$ : $3 \tan ⁣ (x - \frac{π}{3}) = - 3$
Solve on $[0, 2 π)$ : $3 \sin ⁣ (x - \frac{π}{6}) = 3$
Solve on $[0, 2 π)$ : $2 \sin ⁣ (x - \frac{2 π}{3}) = - 2$
Solve on $[0, 2 π)$ : $2 \tan ⁣ (x - \frac{3 π}{4}) = 0$

Solve in degrees to the nearest tenth
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $8 \sin x = - 3$
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $7 \tan x = - 14$
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $2 \cos x = 1$
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $9 \cos x = - 4$



Sigma Prep · sigmaprep.io/worksheets Name Trig EquationsAnswer keyVersion 1 Date Period Solve each equation on [0, 2π) unless another interval is given or it asks for all solutions. Solve basic trig equations on $[0, 2\pi)$ $2 \cos x = 2$ $0$ $2 \sin x = 2$ $\frac{π}{2}$ $\tan x = 1$ $\frac{π}{4}, \frac{5 π}{4}$ $2 \sin x = - 2$ $\frac{3 π}{2}$ Find all solutions Find all solutions: $2 \sin^{2} x = 1$ $x = \frac{π}{4} + π k, \frac{3 π}{4} + π k$ Find all solutions: $3 \cos x = \cos x + \sqrt{2}$ $x = \frac{π}{4} + 2 π k, \frac{7 π}{4} + 2 π k$ Find all solutions: $\tan^{2} x = 3$ $x = \frac{π}{3} + π k, \frac{2 π}{3} + π k$ Find all solutions: $5 \cos x - \sqrt{3} = 3 \cos x$ $x = \frac{π}{6} + 2 π k, \frac{11 π}{6} + 2 π k$ Solve with $\sec$ , $\csc$ and $\cot$ Solve on $[0, 2 π)$ : $5 \csc x - 2 \sqrt{3} = 2 \csc x$ $\frac{π}{3}, \frac{2 π}{3}$ Solve on $[0, 2 π)$ : $\sqrt{3} \cot x + 2 = 1$ $\frac{2 π}{3}, \frac{5 π}{3}$ Solve on $[0, 2 π)$ : $\sqrt{3} \sec x + 5 = 3$ $\frac{5 π}{6}, \frac{7 π}{6}$ Solve on $[0, 2 π)$ : $6 \sec x - 4 \sqrt{3} = - 8 \sqrt{3}$ $\frac{5 π}{6}, \frac{7 π}{6}$ Solve with a shifted angle Solve on $[0, 2 π)$ : $3 \tan ⁣ (x - \frac{π}{3}) = - 3$ $\frac{π}{12}, \frac{13 π}{12}$ Solve on $[0, 2 π)$ : $3 \sin ⁣ (x - \frac{π}{6}) = 3$ $\frac{2 π}{3}$ Solve on $[0, 2 π)$ : $2 \sin ⁣ (x - \frac{2 π}{3}) = - 2$ $\frac{π}{6}$ Solve on $[0, 2 π)$ : $2 \tan ⁣ (x - \frac{3 π}{4}) = 0$ $\frac{3 π}{4}, \frac{7 π}{4}$ Solve in degrees to the nearest tenth Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $8 \sin x = - 3$ ${202.0}^{\circ}, {338.0}^{\circ}$ Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $7 \tan x = - 14$ ${116.6}^{\circ}, {296.6}^{\circ}$ Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $2 \cos x = 1$ ${60.0}^{\circ}, {300.0}^{\circ}$ Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $9 \cos x = - 4$ ${116.4}^{\circ}, {243.6}^{\circ}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Trig EquationsAnswer keyVersion 1

Date Period

Solve each equation on [0, 2π) unless another interval is given or it asks for all solutions.

Solve basic trig equations on $[0, 2\pi)$
$2 \cos x = 2$ $0$
$2 \sin x = 2$ $\frac{π}{2}$
$\tan x = 1$ $\frac{π}{4}, \frac{5 π}{4}$
$2 \sin x = - 2$ $\frac{3 π}{2}$

Find all solutions
Find all solutions: $2 \sin^{2} x = 1$ $x = \frac{π}{4} + π k, \frac{3 π}{4} + π k$
Find all solutions: $3 \cos x = \cos x + \sqrt{2}$ $x = \frac{π}{4} + 2 π k, \frac{7 π}{4} + 2 π k$
Find all solutions: $\tan^{2} x = 3$ $x = \frac{π}{3} + π k, \frac{2 π}{3} + π k$
Find all solutions: $5 \cos x - \sqrt{3} = 3 \cos x$ $x = \frac{π}{6} + 2 π k, \frac{11 π}{6} + 2 π k$

Solve with $\sec$ , $\csc$ and $\cot$
Solve on $[0, 2 π)$ : $5 \csc x - 2 \sqrt{3} = 2 \csc x$ $\frac{π}{3}, \frac{2 π}{3}$
Solve on $[0, 2 π)$ : $\sqrt{3} \cot x + 2 = 1$ $\frac{2 π}{3}, \frac{5 π}{3}$
Solve on $[0, 2 π)$ : $\sqrt{3} \sec x + 5 = 3$ $\frac{5 π}{6}, \frac{7 π}{6}$
Solve on $[0, 2 π)$ : $6 \sec x - 4 \sqrt{3} = - 8 \sqrt{3}$ $\frac{5 π}{6}, \frac{7 π}{6}$

Solve with a shifted angle
Solve on $[0, 2 π)$ : $3 \tan ⁣ (x - \frac{π}{3}) = - 3$ $\frac{π}{12}, \frac{13 π}{12}$
Solve on $[0, 2 π)$ : $3 \sin ⁣ (x - \frac{π}{6}) = 3$ $\frac{2 π}{3}$
Solve on $[0, 2 π)$ : $2 \sin ⁣ (x - \frac{2 π}{3}) = - 2$ $\frac{π}{6}$
Solve on $[0, 2 π)$ : $2 \tan ⁣ (x - \frac{3 π}{4}) = 0$ $\frac{3 π}{4}, \frac{7 π}{4}$

Solve in degrees to the nearest tenth
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $8 \sin x = - 3$ ${202.0}^{\circ}, {338.0}^{\circ}$
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $7 \tan x = - 14$ ${116.6}^{\circ}, {296.6}^{\circ}$
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $2 \cos x = 1$ ${60.0}^{\circ}, {300.0}^{\circ}$
Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $9 \cos x = - 4$ ${116.4}^{\circ}, {243.6}^{\circ}$

How to do these

$2 \cos x + \sqrt{3} = 0$

Cosine is negative root 3 over 2.
The reference angle is pi over 6.
Cosine is negative in the second and third quadrants.

The answer is $\frac{5 π}{6}, \frac{7 π}{6}$ .

Where students go wrong

Stopping at one answer. On a whole turn a sine or cosine equation almost always has two, and with a multiple of x inside there are more still: the interval gets divided as well.

Also called solving trigonometric equations, sin cos tan equations or solving on 0 to 2pi.

What you can put on this worksheet

One ratio equal to one value: $2 \cos x = - 2$ → $π$
All solutions, with + 2πk or + πk: Find all solutions: $\cos x = 1$ → $x = 2 π k$
Secant, cosecant and cotangent: Solve on $[0, 2 π)$ : $\csc x = - \sqrt{2}$ → $\frac{5 π}{4}, \frac{7 π}{4}$
A shifted argument: Solve on $[0, 2 π)$ : $\cos ⁣ (x - \frac{π}{4}) = - \frac{1}{2}$ → $\frac{11 π}{12}, \frac{19 π}{12}$
With a calculator, in degrees: Solve on $[0^{\circ}, 360^{\circ})$ , to the nearest tenth of a degree: $6 \cos x = 1$ → ${80.4}^{\circ}, {279.6}^{\circ}$
Multiple angles, shifts and numbers outside: Solve on $[0, 2 π)$ : $\tan 3 x = 0$ → $0, \frac{π}{3}, \frac{2 π}{3}, π, \frac{4 π}{3}, \frac{5 π}{3}$
All solutions: shifted, multiple-angle and reciprocal: Find all solutions:
$\cos ⁣ (2 x + \frac{π}{4}) = 0$ → $x = \frac{π}{8} + \frac{π k}{2}$

Questions about these worksheets

Yes. Every trig equations 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 trig equations 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 7: one ratio equal to one value, all solutions, with + 2πk or + πk, secant, cosecant and cotangent, a shifted argument, with a calculator, in degrees, multiple angles, shifts and numbers outside and all solutions: shifted, multiple-angle and reciprocal. Tick as many as you want and set how many of each, or let it spread them evenly.

Stopping at one answer. On a whole turn a sine or cosine equation almost always has two, and with a multiple of x inside there are more still: the interval gets divided as well.

Trig equations worksheet for Precalculus

Select your difficulty

Solve basic trig equations on [0,2π)[0, 2\pi)[0,2π)

Find all solutions

Solve with sec⁡\secsec, csc⁡\csccsc and cot⁡\cotcot

Solve with a shifted angle

Solve in degrees to the nearest tenth

Solve basic trig equations on [0,2π)[0, 2\pi)[0,2π)

Find all solutions

Solve with sec⁡\secsec, csc⁡\csccsc and cot⁡\cotcot

Solve with a shifted angle

Solve in degrees to the nearest tenth

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these trig equations worksheets free?+

Do the trig equations worksheets come with an answer key?+

Are these trig equations worksheets printable?+

What grade are these trig equations worksheets for?+

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

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

Can I choose how hard the trig equations questions are?+

What kinds of question are on a trig equations worksheet?+

What do students get wrong with trig equations?+

Solve basic trig equations on $[0, 2\pi)$

Solve with $\sec$ , $\csc$ and $\cot$

Solve basic trig equations on $[0, 2\pi)$

Solve with $\sec$ , $\csc$ and $\cot$