Free Printable WorksheetMathTrigonometryMath CurriculumTRIG.107

TRIG.107 Determine the number of solutions without fully solving Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.107 Determine the number of solutions without fully solving. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.107 Determine the number of solutions without fully solving - Determine the number of solutions without fully solving

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.107 Determine the number of solutions without fully solving skill assessments:

Problem 1Difficulty: Mastery

How many solutions for x in [0, 2π] satisfy: 2·|sin(4x + 0.25π)| + 1 = 3 ?

Solution & Explanation:1) Isolate the trig part: abs(sin(4x + 0.25π)) = 1. 3) Let u = 4x + 0.25π. Then as x goes from 0 to 2π, u runs through [0.25π, 8.25π]. 4) Solve the absolute-value equation by considering both signs: sin(u) = 1 and sin(u) = -1. Count all solutions in the u-interval. 5) Each u-solution corresponds to exactly one x because u is linear in x.

Problem 2Difficulty: Mastery

How many solutions for x in [-0.5π, 2.5π] satisfy: sin(3x - 0.5π) = 0 ?

Solution & Explanation:1) Isolate the trig part: sin(3x - 0.5π) = 0. 3) Let u = 3x - 0.5π. Then as x goes from -0.5π to 2.5π, u runs through [-2π, 7π]. 4) sin(u)=0 happens at u = kπ. Count integers k with kπ in the u-interval. 5) Each u-solution gives exactly one x-solution because u=ax+b is one-to-one on the interval.

Problem 3Difficulty: Mastery

How many solutions for x in [0.1π, 1.3π] satisfy: |cos(5x + 0.5π)| = 0.5 ?

Solution & Explanation:1) Isolate the trig part: abs(cos(5x + 0.5π)) = 0.5. 3) Let u = 5x + 0.5π. Then as x goes from 0.1π to 1.3π, u runs through [π, 7π]. 4) Solve the absolute-value equation by considering both signs: cos(u) = 0.5 and cos(u) = -0.5. Count all solutions in the u-interval. 5) Each u-solution corresponds to exactly one x because u is linear in x.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard TRIG.107 (Determine the number of solutions without fully solving).