Graph y = sec (2x) - 1

Period π, range excludes (-2, 0)

Graph y = -csc (x) - 1

Period 2π, reflected over the x-axis, range excludes (-2, 0)

Graph y = csc (x) - 2

Period 2π, range excludes (-3, -1)

Graph y = -sec (x) + 1

Period 2π, reflected over the x-axis, range excludes (0, 2)

Period 2π, range excludes (-2, 2)

Graph y = -sec (2(x - π/4)) - 2

Period π, reflected over the x-axis, right π/4[-0.85em]0pt2.35em, range excludes (-3, -1)

Graph y = 2sec (2x) + 2

Period π, range excludes (0, 4)

Graph y = csc (x - π/2)

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

Graph y = 2csc (x) + 2

Period 2π, range excludes (0, 4)

Graph y = -csc (x - π/2) - 1

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

Period π, range excludes (-1, 1)

Graph y = csc (2(x - π/4))

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

Graph y = sec (x) + 2

Period 2π, range excludes (1, 3)

Graph y = sec (x - π/2) - 1

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

Graph y = 2csc (2x) - 2

Period π, range excludes (-4, 0)

Graph y = -csc (2(x - π/4)) + 1

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

Graph y = csc (2x) + 2

Period π, range excludes (1, 3)

Graph y = 2sec (x) - 2

Period 2π, range excludes (-4, 0)

Graph y = -csc (2x) + 1

Period π, reflected over the x-axis, range excludes (0, 2)

Worksheets · Precalculus

Graphing secant and cosecant worksheet

Secant is one over cosine, so wherever cosine touches zero the secant flies off, and wherever cosine peaks the secant touches the same height. Sketch the cosine underneath first and the secant traces itself.

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 Secant and Cosecant Date Period Graph each function from 0 to 2π, or answer as asked. Graph $y = \sec (2 x) - 1$ Graph $y = - ⁣ \csc (x) - 1$ Graph $y = \csc (x) - 2$ Graph $y = - ⁣ \sec (x) + 1$ Graph $y = 2 \sec (x)$ Graph $y = - ⁣ \sec ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Graph $y = 2 \sec (2 x) + 2$ Graph $y = \csc ⁣ (x - \frac{π}{2})$ Graph $y = 2 \csc (x) + 2$ Graph $y = - ⁣ \csc ⁣ (x - \frac{π}{2}) - 1$ Graph $y = \sec (2 x)$ Graph $y = \csc ⁣ (2 ⁣ (x - \frac{π}{4}))$ Graph $y = \sec (x) + 2$ Graph $y = \sec ⁣ (x - \frac{π}{2}) - 1$ Graph $y = 2 \csc (2 x) - 2$ Graph $y = - ⁣ \csc ⁣ (2 ⁣ (x - \frac{π}{4})) + 1$ Graph $y = \csc (2 x) + 2$ Graph $y = 2 \sec (x) - 2$ Graph $y = \csc (x)$ Graph $y = - ⁣ \csc (2 x) + 1$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Secant and Cosecant

Date Period

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

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



Sigma Prep · sigmaprep.io/worksheets Name Graphing Secant and CosecantAnswer keyVersion 1 Date Period Graph each function from 0 to 2π, or answer as asked. Graph $y = \sec (2 x) - 1$ Period $π$ , range excludes $(- 2, 0)$ Graph $y = - ⁣ \csc (x) - 1$ Period $2 π$ , reflected over the $x$ -axis, range excludes $(- 2, 0)$ Graph $y = \csc (x) - 2$ Period $2 π$ , range excludes $(- 3, - 1)$ Graph $y = - ⁣ \sec (x) + 1$ Period $2 π$ , reflected over the $x$ -axis, range excludes $(0, 2)$ Graph $y = 2 \sec (x)$ Period $2 π$ , range excludes $(- 2, 2)$ Graph $y = - ⁣ \sec ⁣ (2 ⁣ (x - \frac{π}{4})) - 2$ Period $π$ , reflected over the $x$ -axis, right $\frac{π}{4}$ , range excludes $(- 3, - 1)$ Graph $y = 2 \sec (2 x) + 2$ Period $π$ , range excludes $(0, 4)$ Graph $y = \csc ⁣ (x - \frac{π}{2})$ Period $2 π$ , right $\frac{π}{2}$ , range excludes $(- 1, 1)$ Graph $y = 2 \csc (x) + 2$ Period $2 π$ , range excludes $(0, 4)$ Graph $y = - ⁣ \csc ⁣ (x - \frac{π}{2}) - 1$ Period $2 π$ , reflected over the $x$ -axis, right $\frac{π}{2}$ , range excludes $(- 2, 0)$ Graph $y = \sec (2 x)$ Period $π$ , range excludes $(- 1, 1)$ Graph $y = \csc ⁣ (2 ⁣ (x - \frac{π}{4}))$ Period $π$ , right $\frac{π}{4}$ , range excludes $(- 1, 1)$ Graph $y = \sec (x) + 2$ Period $2 π$ , range excludes $(1, 3)$ Graph $y = \sec ⁣ (x - \frac{π}{2}) - 1$ Period $2 π$ , right $\frac{π}{2}$ , range excludes $(- 2, 0)$ Graph $y = 2 \csc (2 x) - 2$ Period $π$ , range excludes $(- 4, 0)$ Graph $y = - ⁣ \csc ⁣ (2 ⁣ (x - \frac{π}{4})) + 1$ Period $π$ , reflected over the $x$ -axis, right $\frac{π}{4}$ , range excludes $(0, 2)$ Graph $y = \csc (2 x) + 2$ Period $π$ , range excludes $(1, 3)$ Graph $y = 2 \sec (x) - 2$ Period $2 π$ , range excludes $(- 4, 0)$ Graph $y = \csc (x)$ Period $2 π$ , range excludes $(- 1, 1)$ Graph $y = - ⁣ \csc (2 x) + 1$ Period $π$ , reflected over the $x$ -axis, range excludes $(0, 2)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Secant and CosecantAnswer keyVersion 1

Date Period

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

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

How to do these

Graph $y = \sec (x)$

Cosine is zero at pi over 2 and at 3 pi over 2, so those are the asymptotes.
Cosine peaks at 1 when x is 0 and at 2 pi, so the secant touches 1 there.
Each piece opens away from the axis, never entering the band between -1 and 1.

The answer is Period $2 π$ , range excludes $(- 1, 1)$ .

Where students go wrong

Drawing it through the middle like a sine wave. There is a band either side of the axis that a secant never enters, and every piece opens away from it.

Also called secant graphs, cosecant graphs, reciprocal trig graphs or plotting sec and csc.

Questions about these worksheets

Yes. Every graphing secant and cosecant 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 secant and cosecant 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.

Drawing it through the middle like a sine wave. There is a band either side of the axis that a secant never enters, and every piece opens away from it.

Graphing secant and cosecant worksheet

Select your difficulty

How to do these

Where students go wrong

Questions about these worksheets

Are these graphing secant and cosecant worksheets free?+

Do the graphing secant and cosecant worksheets come with an answer key?+

Are these graphing secant and cosecant worksheets printable?+

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Can I get a different version of the same graphing secant and cosecant worksheet?+

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What do students get wrong with graphing secant and cosecant?+