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Trigonometric Equations on Bounded Intervals worksheets

Find all exact sine, cosine, and tangent solutions in explicit half-open radian or degree intervals, including simple frequency and phase transformations.

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Find every distinct exact solution in the stated half-open interval. Check endpoints and exclude values where the original expression is undefined.

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Paper sizes and printing help · More trigonometry activities

Connect identities with exact unit-circle values

Practice reciprocal, quotient, and Pythagorean identities with the original domain stated beside the work. Equation sheets use standard exact sine, cosine, and tangent values within a clearly printed half-open interval.

Learning objective

What this activity builds

Generate the complete distinct exact solution set for a standard-value trigonometric equation on a bounded interval.

Worked example

Solve sin(x)=1/2 for x in [0,2pi).

x=pi/6, 5pi/6.

Sine is 1/2 at the quadrant I and II angles with reference angle pi/6; 2pi is excluded.

Teaching notes

Make the practice count

  • Write the general angle family before filtering the interval.
  • Treat the upper endpoint as excluded.
  • For tangent, mark inputs where cosine is zero before checking candidates.

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Math SheetNameScoreTeacherDateTrigonometric Equations on Bounded IntervalsFind every distinct exact solution in the stated half-open interval. Check endpoints and exclude values where the original expression is undefined.1.Solve sin(x) = -1/2 for all x in [0, 2pi).2.Solve 2 tan(2x - pi/6) = 0 for all x in [0, 2pi).Show exact work and respect the stated original domain.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateTrigonometric Equations on Bounded IntervalsFind every distinct exact solution in the stated half-open interval. Check endpoints and exclude values where the original expression is undefined.3.Solve -sin(3x + pi/4) = -sqrt(3)/2 for all x in [0, 2pi).4.Solve sin(x - pi/3) = sqrt(2)/2 for all x in [0, 2pi).Show exact work and respect the stated original domain.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateTrigonometric Equations on Bounded IntervalsFind every distinct exact solution in the stated half-open interval. Check endpoints and exclude values where the original expression is undefined.5.Solve cos(2x) = -1/2 for all x in [0, 2pi).6.Solve 2 tan(3x - pi/6) = -2sqrt(3)/3 for all x in [0, 2pi).Show exact work and respect the stated original domain.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateTrigonometric Equations on Bounded IntervalsFind every distinct exact solution in the stated half-open interval. Check endpoints and exclude values where the original expression is undefined.7.Solve tan(x + pi/4) = 1 for all x in [0, 2pi).8.Solve 2 cos(2x - pi/3) = sqrt(2) for all x in [0, 2pi).Show exact work and respect the stated original domain.math-sheet.comPage 4 of 4

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