Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.GT.2

TRIG.59 Graph a transformed sine or cosine function from an equation Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.59 Graph a transformed sine or cosine function from an equation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.59 Graph a transformed sine or cosine function from an equation - Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Select the correct graph of a given transformed sine or cosine equation, including key points for one or more periods. 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). 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.59 Graph a transformed sine or cosine function from an equation skill assessments:

Problem 1Difficulty: Mastery

Select the graph of y = (-3/2) cos((9/5)(x + 2pi/9)) - 3/2 over the shown interval. Each choice lists five key points from one full cycle.

AGraph A key points: (-2pi/9, -2); (pi/18, -1/2); (pi/3, 1); (11pi/18, -1/2); (8pi/9, -2)

BGraph B key points: (-2pi/9, -3); (pi/18, -3/2); (pi/3, 0); (11pi/18, -3/2); (8pi/9, -3)

CGraph C key points: (-2pi/9, 0); (pi/18, -3/2); (pi/3, -3); (11pi/18, -3/2); (8pi/9, 0)

DGraph D key points: (2pi/9, -3); (pi/2, -3/2); (7pi/9, 0); (19pi/18, -3/2); (4pi/3, -3)

Solution & Explanation:For y = (-3/2) cos((9/5)(x + 2pi/9)) - 3/2, the amplitude is 3/2, the midline is y = -3/2, and the period is 10pi/9. Starting at x = -2pi/9, the key points are (-2pi/9, -3); (pi/18, -3/2); (pi/3, 0); (11pi/18, -3/2); (8pi/9, -3). Those features match Graph B.

Problem 2Difficulty: Mastery

Which labeled graph has the same amplitude, midline, period, and starting key point as y = sin((9/5)(x - 2pi/9)) + 3? The visual shows two periods; the choices list key points from the first full cycle.

AGraph A key points: (2pi/9, 2); (pi/2, 3); (7pi/9, 2); (19pi/18, 1); (4pi/3, 2)

BGraph B key points: (2pi/9, 3); (pi/2, 5); (7pi/9, 3); (19pi/18, 1); (4pi/3, 3)

CGraph C key points: (2pi/9, 3); (pi/2, 4); (7pi/9, 3); (19pi/18, 2); (4pi/3, 3)

DGraph D key points: (-2pi/9, 3); (pi/18, 4); (pi/3, 3); (11pi/18, 2); (8pi/9, 3)

Solution & Explanation:For y = sin((9/5)(x - 2pi/9)) + 3, the amplitude is 1, the midline is y = 3, and the period is 10pi/9. Starting at x = 2pi/9, the key points are (2pi/9, 3); (pi/2, 4); (7pi/9, 3); (19pi/18, 2); (4pi/3, 3). Those features match Graph C.

Problem 3Difficulty: Mastery

Match the equation y = -5 cos((4/5)(x + 5pi/6)) + 1 to the correct graph in the image. Each choice lists five key points from one full cycle.

AGraph A key points: (-5pi/6, -3); (-5pi/24, 2); (5pi/12, 7); (25pi/24, 2); (5pi/3, -3)

BGraph B key points: (-5pi/6, 6); (-5pi/24, 1); (5pi/12, -4); (25pi/24, 1); (5pi/3, 6)

CGraph C key points: (5pi/6, -4); (35pi/24, 1); (25pi/12, 6); (65pi/24, 1); (10pi/3, -4)

DGraph D key points: (-5pi/6, -4); (-5pi/24, 1); (5pi/12, 6); (25pi/24, 1); (5pi/3, -4)

Solution & Explanation:For y = -5 cos((4/5)(x + 5pi/6)) + 1, the amplitude is 5, the midline is y = 1, and the period is 5pi/2. Starting at x = -5pi/6, the key points are (-5pi/6, -4); (-5pi/24, 1); (5pi/12, 6); (25pi/24, 1); (5pi/3, -4). Those features match Graph D.

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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 UTRI.GT.2 (Primary standard selected for prompt fields in this prompt cell: UTRI.GT.2. Skill statement in this prompt cell: Select the correct graph of a given transformed sine or cosine equation, including key points for one or more periods. 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). Use this prompt-provided wording as the supporting standard description for this workflow.).