Graph y = sin (2(x - π/4)) + 1

Amplitude 1, period π, right π/4[-0.85em]0pt2.35em, up 1

Graph y = -2sin (x) + 1

Amplitude 2, period 2π, reflected over the x-axis, up 1

Graph y = -3sin (2(x - π/4)) - 2

Amplitude 3, period π, reflected over the x-axis, right π/4[-0.85em]0pt2.35em, down 2

Graph y = -3cos (x) - 1

Amplitude 3, period 2π, reflected over the x-axis, down 1

Graph y = -3cos (x - π/2) - 1

Amplitude 3, period 2π, reflected over the x-axis, right π/2[-0.85em]0pt2.35em, down 1

Graph y = 2cos (x - π/2) - 1

Amplitude 2, period 2π, right π/2[-0.85em]0pt2.35em, down 1

Graph y = 3sin (x - π/2)

Amplitude 3, period 2π, right π/2[-0.85em]0pt2.35em

Graph y = -cot (x) - 1

Period π, asymptotes every π, reflected over the x-axis, down 1

Graph y = 2tan (2(x - π/4)) - 2

Period π/2[-0.85em]0pt2.35em, asymptotes every π/2[-0.85em]0pt2.35em, right π/4[-0.85em]0pt2.35em, down 2

Period π/2[-0.85em]0pt2.35em, asymptotes every π/2[-0.85em]0pt2.35em

Graph y = cot (x - π/2)

Period π, asymptotes every π, right π/2[-0.85em]0pt2.35em

Period π, asymptotes every π, reflected over the x-axis

Graph y = 2tan (2x) + 1

Period π/2[-0.85em]0pt2.35em, asymptotes every π/2[-0.85em]0pt2.35em, up 1

Graph y = tan (x - π/2) - 1

Period π, asymptotes every π, right π/2[-0.85em]0pt2.35em, down 1

Graph y = csc (x - π/2) - 2

Period 2π, right π/2[-0.85em]0pt2.35em, range excludes (-3, -1)

Graph y = -sec (x - π/2) - 1

Period 2π, reflected over the x-axis, right π/2[-0.85em]0pt2.35em, range excludes (-2, 0)

Graph y = 2sec (2x) - 1

Period π, range excludes (-3, 1)

Graph y = -csc (x - π/2) - 2

Period 2π, reflected over the x-axis, right π/2[-0.85em]0pt2.35em, range excludes (-3, -1)

Graph y = sec (2(x - π/4)) - 1

Period π, right π/4[-0.85em]0pt2.35em, range excludes (-2, 0)

Graph y = csc (2(x - π/4))

Period π, right π/4[-0.85em]0pt2.35em, range excludes (-1, 1)

Period π/2[-0.85em]0pt2.35em, asymptotes every π/2[-0.85em]0pt2.35em

Period π, range excludes (-2, 2)

Graph: y = 3/2cos (3theta + 5π/6) - 1

Amplitude 3/2 Period 2π/3 Phase shift 5π/18 left Vertical shift 1 down

Graph y = 3sin (-2theta + π/6) - 2 and give the amplitude, period, phase shift and vertical shift.

Amplitude 3; period π; phase shift π/12 right; vertical shift 2 down

y = cot (3theta - π/6) - 3. Give the period, phase shift, vertical shift and two vertical asymptotes.

Period π/3; phase shift π/18 right; vertical shift 3 down; asymptotes theta = π/18, theta = 7π/18

Describe the transformations of y = sin theta that give y = -sin (3theta - 3π/4) - 2

reflect in the x-axis; compress horizontally by a factor of 1/3; shift right π/4; shift down 2

Worksheets · Precalculus

Graphing trig functions worksheet for Precalculus

Six shapes and two things to read off each one: how tall it gets and how often it repeats. The ones with asymptotes ask for those too. Once each is familiar on its own, the work is telling at a glance which of the six you are looking at.

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 Graphing Trig Functions Date Period Graph each function from 0 to 2π, or answer as asked. Graph sine and cosine Graph $y = \sin ⁣ (2 ⁣ (x - \frac{π}{4})) + 1$ Graph $y = - 2 \sin (x) + 1$ Graph $y = - 3 \sin ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Graph $y = - 3 \cos (x) - 1$ Graph $y = - 3 \cos ⁣ (x - \frac{π}{2}) - 1$ Graph $y = 2 \cos ⁣ (x - \frac{π}{2}) - 1$ Graph $y = 3 \sin ⁣ (x - \frac{π}{2})$ Graph tangent and cotangent Graph $y = - ⁣ \cot (x) - 1$ Graph $y = 2 \tan ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Graph $y = \tan (2 x)$ Graph $y = \cot ⁣ (x - \frac{π}{2})$ Graph $y = - ⁣ \tan (x)$ Graph $y = 2 \tan (2 x) + 1$ Graph $y = \tan ⁣ (x - \frac{π}{2}) - 1$ Graph secant and cosecant Graph $y = \csc ⁣ (x - \frac{π}{2}) - 2$ Graph $y = - ⁣ \sec ⁣ (x - \frac{π}{2}) - 1$ Graph $y = 2 \sec (2 x) - 1$ Graph $y = - ⁣ \csc ⁣ (x - \frac{π}{2}) - 2$ Graph $y = \sec ⁣ (2 ⁣ (x - \frac{π}{4})) - 1$ Graph $y = \csc ⁣ (2 ⁣ (x - \frac{π}{4}))$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Trig Functions

Date Period

Graph each function from 0 to 2π, or answer as asked.

Graph sine and cosine
Graph $y = \sin ⁣ (2 ⁣ (x - \frac{π}{4})) + 1$
Graph $y = - 2 \sin (x) + 1$
Graph $y = - 3 \sin ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$
Graph $y = - 3 \cos (x) - 1$
Graph $y = - 3 \cos ⁣ (x - \frac{π}{2}) - 1$
Graph $y = 2 \cos ⁣ (x - \frac{π}{2}) - 1$
Graph $y = 3 \sin ⁣ (x - \frac{π}{2})$

Graph tangent and cotangent
Graph $y = - ⁣ \cot (x) - 1$
Graph $y = 2 \tan ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$
Graph $y = \tan (2 x)$
Graph $y = \cot ⁣ (x - \frac{π}{2})$
Graph $y = - ⁣ \tan (x)$
Graph $y = 2 \tan (2 x) + 1$
Graph $y = \tan ⁣ (x - \frac{π}{2}) - 1$

Graph secant and cosecant
Graph $y = \csc ⁣ (x - \frac{π}{2}) - 2$
Graph $y = - ⁣ \sec ⁣ (x - \frac{π}{2}) - 1$
Graph $y = 2 \sec (2 x) - 1$
Graph $y = - ⁣ \csc ⁣ (x - \frac{π}{2}) - 2$
Graph $y = \sec ⁣ (2 ⁣ (x - \frac{π}{4})) - 1$
Graph $y = \csc ⁣ (2 ⁣ (x - \frac{π}{4}))$



Sigma Prep · sigmaprep.io/worksheets Name Graphing Trig FunctionsAnswer keyVersion 1 Date Period Graph each function from 0 to 2π, or answer as asked. Graph sine and cosine Graph $y = \sin ⁣ (2 ⁣ (x - \frac{π}{4})) + 1$ Amplitude $1$ , period $π$ , right $\frac{π}{4}$ , up $1$ Graph $y = - 2 \sin (x) + 1$ Amplitude $2$ , period $2 π$ , reflected over the $x$ -axis, up $1$ Graph $y = - 3 \sin ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Amplitude $3$ , period $π$ , reflected over the $x$ -axis, right $\frac{π}{4}$ , down $2$ Graph $y = - 3 \cos (x) - 1$ Amplitude $3$ , period $2 π$ , reflected over the $x$ -axis, down $1$ Graph $y = - 3 \cos ⁣ (x - \frac{π}{2}) - 1$ Amplitude $3$ , period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , down $1$ Graph $y = 2 \cos ⁣ (x - \frac{π}{2}) - 1$ Amplitude $2$ , period $2 π$ , right $\frac{π}{2}$ , down $1$ Graph $y = 3 \sin ⁣ (x - \frac{π}{2})$ Amplitude $3$ , period $2 π$ , right $\frac{π}{2}$ Graph tangent and cotangent Graph $y = - ⁣ \cot (x) - 1$ Period $π$ , asymptotes every $π$ , reflected over the $x$ -axis, down $1$ Graph $y = 2 \tan ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$ , right $\frac{π}{4}$ , down $2$ Graph $y = \tan (2 x)$ Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$ Graph $y = \cot ⁣ (x - \frac{π}{2})$ Period $π$ , asymptotes every $π$ , right $\frac{π}{2}$ Graph $y = - ⁣ \tan (x)$ Period $π$ , asymptotes every $π$ , reflected over the $x$ -axis Graph $y = 2 \tan (2 x) + 1$ Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$ , up $1$ Graph $y = \tan ⁣ (x - \frac{π}{2}) - 1$ Period $π$ , asymptotes every $π$ , right $\frac{π}{2}$ , down $1$ Graph secant and cosecant Graph $y = \csc ⁣ (x - \frac{π}{2}) - 2$ Period $2 π$ , right $\frac{π}{2}$ , range excludes $(- 3, - 1)$ Graph $y = - ⁣ \sec ⁣ (x - \frac{π}{2}) - 1$ Period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , range excludes $(- 2, 0)$ Graph $y = 2 \sec (2 x) - 1$ Period $π$ , range excludes $(- 3, 1)$ Graph $y = - ⁣ \csc ⁣ (x - \frac{π}{2}) - 2$ Period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , range excludes $(- 3, - 1)$ Graph $y = \sec ⁣ (2 ⁣ (x - \frac{π}{4})) - 1$ Period $π$ , right $\frac{π}{4}$ , range excludes $(- 2, 0)$ Graph $y = \csc ⁣ (2 ⁣ (x - \frac{π}{4}))$ Period $π$ , right $\frac{π}{4}$ , range excludes $(- 1, 1)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Trig FunctionsAnswer keyVersion 1

Date Period

Graph each function from 0 to 2π, or answer as asked.

Graph sine and cosine
Graph $y = \sin ⁣ (2 ⁣ (x - \frac{π}{4})) + 1$ Amplitude $1$ , period $π$ , right $\frac{π}{4}$ , up $1$
Graph $y = - 2 \sin (x) + 1$ Amplitude $2$ , period $2 π$ , reflected over the $x$ -axis, up $1$
Graph $y = - 3 \sin ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Amplitude $3$ , period $π$ , reflected over the $x$ -axis, right $\frac{π}{4}$ , down $2$
Graph $y = - 3 \cos (x) - 1$ Amplitude $3$ , period $2 π$ , reflected over the $x$ -axis, down $1$
Graph $y = - 3 \cos ⁣ (x - \frac{π}{2}) - 1$ Amplitude $3$ , period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , down $1$
Graph $y = 2 \cos ⁣ (x - \frac{π}{2}) - 1$ Amplitude $2$ , period $2 π$ , right $\frac{π}{2}$ , down $1$
Graph $y = 3 \sin ⁣ (x - \frac{π}{2})$ Amplitude $3$ , period $2 π$ , right $\frac{π}{2}$

Graph tangent and cotangent
Graph $y = - ⁣ \cot (x) - 1$ Period $π$ , asymptotes every $π$ , reflected over the $x$ -axis, down $1$
Graph $y = 2 \tan ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$ , right $\frac{π}{4}$ , down $2$
Graph $y = \tan (2 x)$ Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$
Graph $y = \cot ⁣ (x - \frac{π}{2})$ Period $π$ , asymptotes every $π$ , right $\frac{π}{2}$
Graph $y = - ⁣ \tan (x)$ Period $π$ , asymptotes every $π$ , reflected over the $x$ -axis
Graph $y = 2 \tan (2 x) + 1$ Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$ , up $1$
Graph $y = \tan ⁣ (x - \frac{π}{2}) - 1$ Period $π$ , asymptotes every $π$ , right $\frac{π}{2}$ , down $1$

Graph secant and cosecant
Graph $y = \csc ⁣ (x - \frac{π}{2}) - 2$ Period $2 π$ , right $\frac{π}{2}$ , range excludes $(- 3, - 1)$
Graph $y = - ⁣ \sec ⁣ (x - \frac{π}{2}) - 1$ Period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , range excludes $(- 2, 0)$
Graph $y = 2 \sec (2 x) - 1$ Period $π$ , range excludes $(- 3, 1)$
Graph $y = - ⁣ \csc ⁣ (x - \frac{π}{2}) - 2$ Period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , range excludes $(- 3, - 1)$
Graph $y = \sec ⁣ (2 ⁣ (x - \frac{π}{4})) - 1$ Period $π$ , right $\frac{π}{4}$ , range excludes $(- 2, 0)$
Graph $y = \csc ⁣ (2 ⁣ (x - \frac{π}{4}))$ Period $π$ , right $\frac{π}{4}$ , range excludes $(- 1, 1)$

How to do these

Graph $y = 2 \sin (2 x)$

Sine, so it starts at the midline and rises.
The 2 in front is the amplitude, so it reaches 2 either way.
The 2 inside halves the period to pi.

The answer is Amplitude $2$ , period $π$ .

Where students go wrong

Treating them all the same way. Sine and cosine have an amplitude and no asymptotes; tangent and cotangent have asymptotes and no amplitude; secant and cosecant have both asymptotes and a band they never enter.

Also called graphing trigonometric functions, trig graphs or sine cosine tangent graphs.

What you can put on this worksheet

Sine and cosine: Graph $y = 3 \sin (2 x)$ → Amplitude $3$ , period $π$
Tangent and cotangent: Graph $y = 2 \tan (2 x)$ → Period $\frac{π}{2}$ , asymptotes every $\frac{π}{2}$
Secant and cosecant: Graph $y = 2 \sec (2 x)$ → Period $π$ , range excludes $(- 2, 2)$
Shifts from an unfactored argument, fraction amplitudes, sec and csc: Graph:
$y = \frac{3}{2} \cos ⁣ (3 θ + \frac{5 π}{6}) - 1$ → Amplitude $\frac{3}{2}$ Period $\frac{2 π}{3}$ Phase shift $\frac{5 π}{18}$ leftVertical shift $1$ down
A negative inner coefficient, unfactored: Graph $y = 3 \sin ⁣ (- 2 θ + \frac{π}{6}) - 2$ and give the amplitude, period, phase shift and vertical shift. → Amplitude $3$ ; period $π$ ; phase shift $\frac{π}{12}$ right; vertical shift $2$ down
tan and cot, unfactored: two asymptotes: $y = \cot ⁣ (3 θ - \frac{π}{6}) - 3$ . Give the period, phase shift, vertical shift and two vertical asymptotes. → Period $\frac{π}{3}$ ; phase shift $\frac{π}{18}$ right; vertical shift $3$ down; asymptotes $θ = \frac{π}{18}, θ = \frac{7 π}{18}$
Describe the transformations in order: Describe the transformations of $y = \sin θ$ that give $y = - ⁣ \sin ⁣ (3 θ - \frac{3 π}{4}) - 2$ → reflect in the $x$ -axis; compress horizontally by a factor of $\frac{1}{3}$ ; shift right $\frac{π}{4}$ ; shift down $2$

Questions about these worksheets

Yes. Every graphing 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 graphing 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 7: sine and cosine, tangent and cotangent, secant and cosecant, shifts from an unfactored argument, fraction amplitudes, sec and csc, a negative inner coefficient, unfactored, tan and cot, unfactored: two asymptotes and describe the transformations in order. Tick as many as you want and set how many of each, or let it spread them evenly.

Graphing trig functions worksheet for Precalculus

Select your difficulty

Graph sine and cosine

Graph tangent and cotangent

Graph secant and cosecant

Graph sine and cosine

Graph tangent and cotangent

Graph secant and cosecant

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these graphing trig functions worksheets free?+

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

Are these graphing trig functions worksheets printable?+

What grade are these graphing trig functions worksheets for?+

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

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

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

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

What do students get wrong with graphing trig functions?+