Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.GT.2

TRIG.60 Write an equation for a sinusoidal function from key features Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.60 Write an equation for a sinusoidal function from key features. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.60 Write an equation for a sinusoidal function from key features - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Select the equation that matches a given sinusoidal graph, table, or context using amplitude, period, phase shift, and midline. Associated standards listed with this skill in this prompt cell: UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G); UTRI.GT.3; CCSS HSF.TF.B.5; FL MA.912.T.3.3,3.5; VA T.GT.1e. 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.60 Write an equation for a sinusoidal function from key features skill assessments:

Problem 1Difficulty: Mastery
A graph shows a sinusoid with amplitude 1.2, midline y = 4.5, period 18, and a minimum at t = -3. Which equation matches?
Ay = -1.2 cos((pi/9)(t + 3)) + 4.5
By = -1.2 cos((pi/18)(t + 3)) + 4.5
Cy = -1.2 cos((pi/9)(t + 3)) + 3.3
Dy = -1.2 cos((pi/9)(t - 3)) + 4.5
Solution & Explanation:The amplitude is 1.2, the midline is y = 4.5, and the period is 18 units. The minimum at -3 uses negative cosine shifted left 3, and the period 18 gives angular factor pi/9. This matches y = -1.2 cos((pi/9)(t + 3)) + 4.5.
Problem 2Difficulty: Mastery
Table values show x = -pi/5, 0, pi/5, 2pi/5, 3pi/5; y = 0, -6, 0, 6, 0. Which equation matches the table?
Ay = -6 sin((2/5)(x + pi/5))
By = -6 sin((5/2)(x + pi/5))
Cy = -6 sin((5/2)(x + pi/5)) + 6
Dy = -6 sin((5/2)(x - pi/5))
Solution & Explanation:The amplitude is 6, the midline is y = 0, and the period is 4pi/5. The table starts on the midline and moves downward; the period is 4pi/5, giving factor 5/2. This matches y = -6 sin((5/2)(x + pi/5)).
Problem 3Difficulty: Mastery
A sinusoid has range [-12, -4], period pi/6, and a maximum at x = -pi/12. Which equation matches?
Ay = 4 cos(6(x + pi/12)) - 8
By = 4 cos(12(x + pi/12)) - 12
Cy = 4 cos(12(x + pi/12)) - 8
Dy = 4 cos(12(x - pi/12)) - 8
Solution & Explanation:The amplitude is 4, the midline is y = -8, and the period is pi/6. The range gives amplitude 4 and midline -8; period pi/6 gives factor 12; maximum at -pi/12 sets the shift. This matches y = 4 cos(12(x + pi/12)) - 8.

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Frequently Asked Questions

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QIs this TRIG.60 Write an equation for a sinusoidal function from key features worksheet free for teachers and homeschoolers?

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QCan students practice TRIG.60 Write an equation for a sinusoidal function from key features online with instant feedback?

Yes! In addition to this printable worksheet, students can practice TRIG.60 Write an equation for a sinusoidal function from key features 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.GT.2 (Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Select the equation that matches a given sinusoidal graph, table, or context using amplitude, period, phase shift, and midline. Associated standards listed with this skill in this prompt cell: UTRI.GT.2; CCSS HSF.TF.B.5; VA T.GT.1c-d; NY AII-F.BF.3; TEKS §111.42(c)(2)(G); UTRI.GT.3; CCSS HSF.TF.B.5; FL MA.912.T.3.3,3.5; VA T.GT.1e. Use this prompt-provided wording as the supporting standard description for this workflow.).

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