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Trigonometry practice

Basic Trigonometric Identities worksheets

Simplify and verify finite reciprocal, quotient, and Pythagorean identity recipes with the original-domain restrictions made explicit.

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Simplify or verify each identity. State the restrictions from the original expression and show the named identity used at each step.

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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

Use named basic identities to produce valid simplifications and bounded proofs on the original domain.

Worked example

Simplify (1 - cos^2(x))/sin(x).

sin(x), provided sin(x) != 0.

Replace 1 - cos^2(x) with sin^2(x), then cancel one sine only on the original domain.

Teaching notes

Make the practice count

  • Write restrictions before cancelling a factor.
  • Name the reciprocal, quotient, or Pythagorean identity used.
  • Check a claimed identity at several valid angles as an arithmetic check, not as the proof.

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Math SheetNameScoreTeacherDateBasic Trigonometric IdentitiesSimplify or verify each identity. State the restrictions from the original expression and show the named identity used at each step.1.Verify sin(2x)/cos(2x) = tan(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________2.Simplify 1/cos(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________Show exact work and respect the stated original domain.math-sheet.comPage 1 of 4
Math SheetNameScoreTeacherDateBasic Trigonometric IdentitiesSimplify or verify each identity. State the restrictions from the original expression and show the named identity used at each step.3.Verify 1 + tan^2(2x) = sec^2(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________4.Simplify (1 - cos^2(2x))/sin(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________Show exact work and respect the stated original domain.math-sheet.comPage 2 of 4
Math SheetNameScoreTeacherDateBasic Trigonometric IdentitiesSimplify or verify each identity. State the restrictions from the original expression and show the named identity used at each step.5.Verify 1 - sin^2(2x) = cos^2(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________6.Simplify cos(2x)/sin(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________Show exact work and respect the stated original domain.math-sheet.comPage 3 of 4
Math SheetNameScoreTeacherDateBasic Trigonometric IdentitiesSimplify or verify each identity. State the restrictions from the original expression and show the named identity used at each step.7.Verify (sec^2(2x) - 1)/tan(2x) = tan(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________8.Simplify 1/sin(2x). State the original-domain restrictions.Original-domain restrictions: ______________________________Show exact work and respect the stated original domain.math-sheet.comPage 4 of 4

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