Free Printable WorksheetMathTrigonometryMath CurriculumTRIG.69

TRIG.69 Evaluate the reasonableness and limitations of a periodic model Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.69 Evaluate the reasonableness and limitations of a periodic model. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.69 Evaluate the reasonableness and limitations of a periodic model - Evaluate the reasonableness and limitations of a periodic model

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.69 Evaluate the reasonableness and limitations of a periodic model skill assessments:

Problem 1Difficulty: Mastery

A daily periodic model predicts electricity use by clock time. In many places, clocks shift by 1 hour for daylight saving time. How can that affect validity?

AElectricity use cannot be measured on Sundays

BA sine function cannot handle time shifts

CThe same clock time may correspond to different sunlight and routine conditions, shifting the pattern relative to the model

DDaylight saving time changes the value of pi

Solution & Explanation:A clock shift changes how routines line up with clock time, effectively shifting the phase of a daily pattern. A model that ignores this can mispredict around the time change.

Problem 2Difficulty: Mastery

A periodic model is built from data that show only one complete cycle. To use it for long-term prediction, which assumption is most critical?

AThat time starts at zero

BThat the next cycles will match the observed cycle closely (same period, amplitude, and shape)

CThat the graph is smooth

DThat the function is a cosine function

Solution & Explanation:With only one cycle observed, you must assume the behavior truly repeats in future cycles. If the period or amplitude changes, long-term predictions will be unreliable.

Problem 3Difficulty: Mastery

A Ferris wheel model uses t = seconds since 12:00 PM. But the ride being modeled actually starts at 12:05 PM, and the model was fit to data starting when the ride begins. Which fix is most reasonable?

AKeep t as seconds since noon; it does not matter

BMake t negative for times after 12:05 PM

CRedefine the input as minutes after the start of the ride, or replace t with (t - 300) seconds

DReplace sine with cosine; that fixes the start time automatically

Solution & Explanation:If the ride starts 5 minutes after noon, the model's time variable should be aligned to the ride start. 5 minutes is 300 seconds, so shifting by 300 seconds matches the intended domain.

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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.69 (Evaluate the reasonableness and limitations of a periodic model).