Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.EQ.3

TRIG.102 Solve trigonometric inequalities on a given interval Worksheet

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Q: What grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard UTRI.EQ.3 (Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.3. Skill statement in this prompt cell: Select the correct interval solution for where a trig function is greater than or less than a constant on a given interval. Associated standards listed with this skill in this prompt cell: UTRI.EQ.3; VA T.IE.3b; CCSS HSF.IF.B.4. Use this prompt-provided wording as the supporting standard description for this workflow.).

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.102 Solve trigonometric inequalities on a given interval. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.102 Solve trigonometric inequalities on a given interval - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.3. Skill statement in this prompt cell: Select the correct interval solution for where a trig function is greater than or less than a constant on a given interval. Associated standards listed with this skill in this prompt cell: UTRI.EQ.3; VA T.IE.3b; CCSS HSF.IF.B.4. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Trigonometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related TRIG.102 Solve trigonometric inequalities on a given interval skill assessments:

Problem 1Difficulty: Mastery

Which values of x in -2pi <= x <= 2pi satisfy the inequality tan(3x/2 + pi/6) >= -sqrt(3)/3?

A(-2pi, -16pi/9] U (-14pi/9, -10pi/9] U (-8pi/9, -4pi/9] U (-2pi/9, 2pi/9] U (4pi/9, 8pi/9] U (10pi/9, 14pi/9] U (16pi/9, 2pi)

B[-2pi, -16pi/9) U [-14pi/9, -10pi/9) U [-8pi/9, -4pi/9) U [-2pi/9, 2pi/9) U [4pi/9, 8pi/9) U [10pi/9, 14pi/9) U [16pi/9, 2pi]

C(-16pi/9, -14pi/9] U (-10pi/9, -8pi/9] U (-4pi/9, -2pi/9] U (2pi/9, 4pi/9] U (8pi/9, 10pi/9] U (14pi/9, 16pi/9]

D[-2pi, -16pi/9) U (-14pi/9, -10pi/9) U (-8pi/9, -4pi/9) U (-2pi/9, 2pi/9) U (4pi/9, 8pi/9) U (10pi/9, 14pi/9) U (16pi/9, 2pi]

Solution & Explanation:Find the tangent boundary angles and remember that tangent has vertical asymptotes. On -2pi <= x <= 2pi, the intervals that satisfy the inequality are [-2pi, -16pi/9) U [-14pi/9, -10pi/9) U [-8pi/9, -4pi/9) U [-2pi/9, 2pi/9) U [4pi/9, 8pi/9) U [10pi/9, 14pi/9) U [16pi/9, 2pi].

Problem 2Difficulty: Mastery

A student is solving on -2pi <= x <= 2pi. Which interval set makes cos(3x/2 - pi/3) <= sqrt(3)/2 true?

A(-2pi, -11pi/9) U (-pi, pi/9) U (pi/3, 13pi/9) U (5pi/3, 2pi)

B[-11pi/9, -pi] U [pi/9, pi/3] U [13pi/9, 5pi/3]

C[-2pi, -11pi/9] U [-pi, pi/9] U [pi/3, 13pi/9] U [5pi/3, 2pi]

D[-2pi, -11pi/9) U (-pi, pi/9) U (pi/3, 13pi/9) U (5pi/3, 2pi]

Solution & Explanation:Find the angles where cos(3x/2 - pi/3) equals sqrt(3)/2, then use the cosine sign and reference-angle behavior on -2pi <= x <= 2pi. The inequality is true on [-2pi, -11pi/9] U [-pi, pi/9] U [pi/3, 13pi/9] U [5pi/3, 2pi].

Problem 3Difficulty: Mastery

For -2pi <= x <= 2pi, select the interval solution for sin(3x/2 + pi/2) > -sqrt(2)/2.

A[-11pi/6, -5pi/6] U [-pi/2, pi/2] U [5pi/6, 11pi/6]

B[-2pi, -11pi/6) U (-5pi/6, -pi/2) U (pi/2, 5pi/6) U (11pi/6, 2pi]

C(-3pi/2, -7pi/6) U (-pi/6, pi/6) U (7pi/6, 3pi/2)

D(-11pi/6, -5pi/6) U (-pi/2, pi/2) U (5pi/6, 11pi/6)

Solution & Explanation:Find the angles where sin(3x/2 + pi/2) equals -sqrt(2)/2, then use the sine sign and reference-angle behavior on -2pi <= x <= 2pi. The inequality is true on (-11pi/6, -5pi/6) U (-pi/2, pi/2) U (5pi/6, 11pi/6).

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this TRIG.102 Solve trigonometric inequalities on a given interval worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this TRIG.102 Solve trigonometric inequalities on a given interval worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice TRIG.102 Solve trigonometric inequalities on a given interval online with instant feedback?

Yes! In addition to this printable worksheet, students can practice TRIG.102 Solve trigonometric inequalities on a given interval interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard UTRI.EQ.3 (Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.3. Skill statement in this prompt cell: Select the correct interval solution for where a trig function is greater than or less than a constant on a given interval. Associated standards listed with this skill in this prompt cell: UTRI.EQ.3; VA T.IE.3b; CCSS HSF.IF.B.4. Use this prompt-provided wording as the supporting standard description for this workflow.).