Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.EQ.1

TRIG.50 Find all angles in an interval with a given trig value Worksheet

Q: How do I download and print this TRIG.50 Find all angles in an interval with a given trig value worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

Q: Is this TRIG.50 Find all angles in an interval with a given trig value worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

Q: Can students practice TRIG.50 Find all angles in an interval with a given trig value online with instant feedback?

Yes! In addition to this printable worksheet, students can practice TRIG.50 Find all angles in an interval with a given trig value interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

Q: What grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard UTRI.EQ.1 (Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select all angles in a specified interval that satisfy a given sine, cosine, or tangent value. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.).

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.50 Find all angles in an interval with a given trig value. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.50 Find all angles in an interval with a given trig value - Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select all angles in a specified interval that satisfy a given sine, cosine, or tangent value. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. 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.50 Find all angles in an interval with a given trig value skill assessments:

Problem 1Difficulty: Mastery

What is the complete set of angles theta, measured in degrees, satisfying tan(theta) = sqrt(3) on -1020 degrees <= theta <= 1020 degrees?

A-1020 degrees, -840 degrees, -660 degrees, -480 degrees, -300 degrees, -120 degrees, 60 degrees, 240 degrees, 420 degrees, 600 degrees, 780 degrees

B-840 degrees, -660 degrees, -480 degrees, -300 degrees, -120 degrees, 60 degrees, 240 degrees, 420 degrees, 600 degrees, 780 degrees, 960 degrees

C-1020 degrees, -660 degrees, -300 degrees, 60 degrees, 420 degrees, 780 degrees

D-1020 degrees, -840 degrees, -660 degrees, -480 degrees, -300 degrees, -120 degrees, 60 degrees, 240 degrees, 420 degrees, 600 degrees, 780 degrees, 960 degrees

Solution & Explanation:For tan(theta) = sqrt(3), the basic solution pattern is 60 degrees. Because tan repeats every 180 degrees, shift those angles by whole periods and keep only values in -1020 degrees <= theta <= 1020 degrees. The complete solution set is -1020 degrees, -840 degrees, -660 degrees, -480 degrees, -300 degrees, -120 degrees, 60 degrees, 240 degrees, 420 degrees, 600 degrees, 780 degrees, 960 degrees.

Problem 2Difficulty: Mastery

Identify every theta, measured in radians, that matches cos(theta) = -sqrt(2)/2, given -15pi/4 <= theta <= 17pi/4.

A-13pi/4, -11pi/4, -5pi/4, -3pi/4, 3pi/4, 5pi/4, 11pi/4

B-13pi/4, -11pi/4, -5pi/4, -3pi/4, 3pi/4, 5pi/4, 11pi/4, 13pi/4

C-11pi/4, -5pi/4, -3pi/4, 3pi/4, 5pi/4, 11pi/4, 13pi/4

D-13pi/4, -5pi/4, 3pi/4, 11pi/4

Solution & Explanation:For cos(theta) = -sqrt(2)/2, the basic solution pattern is 3pi/4, 5pi/4. Because cos repeats every 2pi, shift those angles by whole periods and keep only values in -15pi/4 <= theta <= 17pi/4. The complete solution set is -13pi/4, -11pi/4, -5pi/4, -3pi/4, 3pi/4, 5pi/4, 11pi/4, 13pi/4.

Problem 3Difficulty: Mastery

For theta measured in degrees, use reference angles and period shifts to solve sin(theta) = 1/2 on -1260 degrees <= theta <= 300 degrees.

A-1050 degrees, -930 degrees, -690 degrees, -570 degrees, -330 degrees, -210 degrees, 30 degrees

B-930 degrees, -690 degrees, -570 degrees, -330 degrees, -210 degrees, 30 degrees, 150 degrees

C-1050 degrees, -690 degrees, -330 degrees, 30 degrees

D-1050 degrees, -930 degrees, -690 degrees, -570 degrees, -330 degrees, -210 degrees, 30 degrees, 150 degrees

Solution & Explanation:For sin(theta) = 1/2, the basic solution pattern is 30 degrees, 150 degrees. Because sin repeats every 360 degrees, shift those angles by whole periods and keep only values in -1260 degrees <= theta <= 300 degrees. The complete solution set is -1050 degrees, -930 degrees, -690 degrees, -570 degrees, -330 degrees, -210 degrees, 30 degrees, 150 degrees.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this TRIG.50 Find all angles in an interval with a given trig value worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this TRIG.50 Find all angles in an interval with a given trig value worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice TRIG.50 Find all angles in an interval with a given trig value online with instant feedback?

Yes! In addition to this printable worksheet, students can practice TRIG.50 Find all angles in an interval with a given trig value 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.EQ.1 (Primary standard selected for prompt fields in this prompt cell: UTRI.EQ.1. Skill statement in this prompt cell: Select all angles in a specified interval that satisfy a given sine, cosine, or tangent value. Associated standards listed with this skill in this prompt cell: UTRI.EQ.1; CCSS HSF.TF.B.7 (+); FL MA.912.T.1.8; VA T.IE.3a; UTRI.UC.3; CCSS HSF.TF.A.4 (+); NY AII-F.TF.4; MA F-TF.A.4. Use this prompt-provided wording as the supporting standard description for this workflow.).