Small practice
brighter futures.
Checking sign-in status
Menu

Precalculus practice

Advanced Trigonometric Equations

Solve factored, quadratic-in-form, identity-rewrite, double-angle, and multiple-angle equations over bounded or general scopes.

Ready-made English PDF · fixed settings

Worksheet · LetterWorksheet · A4
Customize worksheet ↓
With answer key

Customization below makes a separate PDF.

First page of the advanced trigonometric equations 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

Factor or rewrite first, list every solution in the requested scope, and reject values where the original equation is undefined.

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

List every valid solution and reject candidates where the original trig expression is undefined.

Worked example

Solve 2sin^2(x)-sin(x)-1=0 on 0<=x<2pi.

x=pi/2, 7pi/6, 11pi/6.

Factor as (2sin x+1)(sin x-1)=0 and list both standard-value families.

Teaching notes

Make the practice count

  • Solve the algebraic equation in the trig value first.
  • For multiple angles, solve across the expanded angle interval.
  • Substitute candidates into the original equation when denominators occur.

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

Equation forms
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 · Advanced Trigonometric Equations · US Letter

Preview ready. Download includes these exact pages.

4 student pages
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScoreTeacherDateAdvanced Trigonometric EquationsFactor or rewrite first, list every solution in the requested scope, and reject values where the original equation is undefined.1. Solve cos(3(x - 5pi/12))=0 for all real x.Assumptions: General solutions use integer n and retain all original undefined points.2. Solve cos(2(x - pi/12))=0 on 0 <= x < 2pi.Assumptions: The interval is half-open, so include its left endpoint and exclude its right endpoint.Show exact work and preserve every stated domain restriction.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateAdvanced Trigonometric EquationsFactor or rewrite first, list every solution in the requested scope, and reject values where the original equation is undefined.3. Solve cos((x - 3pi/4))[2cos((x - 3pi/4))-1]=0 on 0 <= x < 2pi.Assumptions: The interval is half-open, so include its left endpoint and exclude its right endpoint.4. Solve 2cos^2((x - 5pi/6))+cos((x - 5pi/6))-1=0 on 0 <= x < 2pi.Assumptions: The interval is half-open, so include its left endpoint and exclude its right endpoint.Show exact work and preserve every stated domain restriction.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateAdvanced Trigonometric EquationsFactor or rewrite first, list every solution in the requested scope, and reject values where the original equation is undefined.5. Solve sin(3(x - pi/2))=0 for all real x.Assumptions: General solutions use integer n and retain all original undefined points.6. Solve tan(2(x - pi/4))=0 for all real x.Assumptions: General solutions use integer n and retain all original undefined points.Show exact work and preserve every stated domain restriction.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateAdvanced Trigonometric EquationsFactor or rewrite first, list every solution in the requested scope, and reject values where the original equation is undefined.7. Solve tan((x - 11pi/12))[tan((x - 11pi/12))-1]=0 on 0 <= x < 2pi.Assumptions: The interval is half-open, so include its left endpoint and exclude its right endpoint.8. Solve sin(2(x - 2pi/3))=0 on 0 <= x < 2pi.Assumptions: The interval is half-open, so include its left endpoint and exclude its right endpoint.Show exact work and preserve every stated domain restriction.math-sheet.comPage 4 of 4

A useful next step

Related activities

Printable sinusoidal modeling preview

Precalculus

Sinusoidal Modeling

Build exact sine or cosine models from noiseless extrema, tables, or graphs in circular, tide, seasonal, and harmonic contexts.

Preview and download