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TRIG.134 Eliminate the parameter when conversion is feasible Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.134 Eliminate the parameter when conversion is feasible. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.134 Eliminate the parameter when conversion is feasible - Eliminate the parameter when conversion is feasible

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Grade

Trigonometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related TRIG.134 Eliminate the parameter when conversion is feasible skill assessments:

Problem 1Difficulty: Mastery

Eliminate t: x = 2cos t + sin t, y = cos t + 2sin t, with 0.5π ≤ t ≤ π. Choose the equation and restriction.

A5x² − 8xy + 5y² = 9, with 2x − y ≥ 0 and −x + 2y ≥ 0

B5x² + 8xy + 5y² = 9, with 2x − y ≤ 0 and −x + 2y ≥ 0

C5x² − 8xy + 5y² = 25, with 2x − y ≤ 0 and −x + 2y ≥ 0

D5x² − 8xy + 5y² = 9, with 2x − y ≤ 0 and −x + 2y ≥ 0

Solution & Explanation:From the inverse relations, cos t = (2x − y)⁄3 and sin t = (−x + 2y)⁄3, giving 5x² − 8xy + 5y² = 9. On 0.5π ≤ t ≤ π, cos t ≤ 0 and sin t ≥ 0, so 2x − y ≤ 0 and −x + 2y ≥ 0.

Problem 2Difficulty: Mastery

Eliminate t: x = 2cos t, y = 2cos(6t), with 0 ≤ t ≤ π. Pick the equation and x‑restriction.

Ay = x⁶ − 6x⁴ + 9x² + 2, with −2 ≤ x ≤ 2

By = x⁶ − 4x⁴ + 9x² − 2, with −2 ≤ x ≤ 2

Cy = x⁶ − 6x⁴ + 9x² − 2, with −2 ≤ x ≤ 2

Dy = x⁶ − 6x⁴ + 9x² − 2, with 0 ≤ x ≤ 2

Solution & Explanation:Let c = cos t = x⁄2. Use cos(6t) = 32c⁶ − 48c⁴ + 18c² − 1. Then y = 2cos(6t) becomes y = 64c⁶ − 96c⁴ + 36c² − 2, which simplifies to y = x⁶ − 6x⁴ + 9x² − 2 after substituting c = x⁄2. Also −2 ≤ x ≤ 2.

Problem 3Difficulty: Mastery

Eliminate t: x = 2sin t, y = 2sin(3t), with 0 ≤ t ≤ π. Choose the equation and x‑restriction.

Ay = x³ − 3x, with 0 ≤ x ≤ 2

By = 3x − x³, with 0 ≤ x ≤ 2

Cy = 3x − x³, with −2 ≤ x ≤ 2

Dy = 3x + x³, with 0 ≤ x ≤ 2

Solution & Explanation:Let s = sin t = x⁄2. Using sin(3t) = 3s − 4s³, we get y = 2(3s − 4s³) = 3x − x³. Because 0 ≤ t ≤ π gives s ≥ 0, we have 0 ≤ x ≤ 2.

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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.134 (Eliminate the parameter when conversion is feasible).