Small practice
brighter futures.
Checking sign-in status
Menu

Precalculus practice

Tangent, Cotangent, Secant, and Cosecant Graphs

Analyze, draw, and write transformed reciprocal-trigonometric graphs with numerical scales, exact anchors, periods, and vertical asymptotes.

Ready-made English PDF · fixed settings

Worksheet · LetterWorksheet · A4
Customize worksheet ↓
With answer key

Customization below makes a separate PDF.

First page of the tangent, cotangent, secant, and cosecant graphs printable worksheetOpen full-size sample (first page)

Fixed English ready-made files. Custom settings below apply only to the configured PDF.

Ready to print

Start with a ready-made worksheet

Mark every vertical asymptote, zero or vertex, and draw each branch without crossing an asymptote. State the period and domain exclusions.

Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.

US Letter

Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
Customize this worksheet

Paper sizes and printing help · More precalculus activities

Keep exact structure and restrictions visible

These worksheets pair exact algebra with labeled graph scales, explicit domains, bounded intervals, and model assumptions. The generated teacher key uses the same resolved task document as the student preview.

Learning objective

What this activity builds

Graph tangent, cotangent, secant, and cosecant by separating branches at every domain exclusion.

Worked example

Graph y=tan(x) over two periods.

Zeros occur at integer multiples of pi and asymptotes at pi/2+kpi.

Each increasing branch lies strictly between consecutive vertical asymptotes.

Teaching notes

Make the practice count

  • Draw asymptotes before curves.
  • Use secant and cosecant vertices where cosine or sine equals plus or minus one.
  • Never connect branches across excluded x-values.

Make it yours

Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose the task families and representations to practice. All controls are bounded; keep the seed to reproduce the same numerical givens.

Worksheet settings

Functions
Page note and reproducible seed

The same settings and seed make the same questions. Shared links include your page note; leave personal information out.

Configured PDF · Graphs of Tangent, Cotangent, Secant, and Cosecant · US Letter

Preview ready. Download includes these exact pages.

3 student pages
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScoreTeacherDateGraphs of Tangent, Cotangent, Secant, and CosecantMark every vertical asymptote, zero or vertex, and draw each branch without crossing an asymptote. State the period and domain exclusions.1. Graph y = csc(x) over the displayed two-period window.Assumptions: Angles use the selected unit. The graph window spans two complete periods, and disconnected branches stop at vertical asymptotes.-5pi/4-8-pi/4-43pi/407pi/4411pi/482. Graph y = sec(x) over the displayed two-period window.Assumptions: Angles use the selected unit. The graph window spans two complete periods, and disconnected branches stop at vertical asymptotes.-7pi/4-8-3pi/4-4pi/405pi/449pi/48Show exact work and preserve every stated domain restriction.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateGraphs of Tangent, Cotangent, Secant, and CosecantMark every vertical asymptote, zero or vertex, and draw each branch without crossing an asymptote. State the period and domain exclusions.3. Write one valid equation for the displayed graph.Assumptions: Angles use the selected unit. The graph window spans two complete periods, and disconnected branches stop at vertical asymptotes.-2pi-8-pi-400pi42pi84. Graph y = 3tan(2(x - pi/4)) - 2 over the displayed two-period window.Assumptions: Angles use the selected unit. The graph window spans two complete periods, and disconnected branches stop at vertical asymptotes.-pi/4-80-4pi/40pi/243pi/48Show exact work and preserve every stated domain restriction.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateGraphs of Tangent, Cotangent, Secant, and CosecantMark every vertical asymptote, zero or vertex, and draw each branch without crossing an asymptote. State the period and domain exclusions.5. Write one valid equation for the displayed graph.Assumptions: Angles use the selected unit. The graph window spans two complete periods, and disconnected branches stop at vertical asymptotes.-3pi/4-8-pi/4-4pi/403pi/445pi/486. Graph y = 2cot(2(x - -pi/8)) - 2 over the displayed two-period window.Assumptions: Angles use the selected unit. The graph window spans two complete periods, and disconnected branches stop at vertical asymptotes.-5pi/8-8-3pi/8-4-pi/80pi/843pi/88Show exact work and preserve every stated domain restriction.math-sheet.comPage 3 of 3

A useful next step

Related activities

Printable advanced trigonometric identities preview

Precalculus

Advanced Trigonometric Identities

Apply sum, difference, double-angle, half-angle, power-reduction, and product-sum identities with explicit domain and sign conditions.

Preview and download