Blurred Lines

Learning Resource Type

Classroom Resource

Subject Area

English Language Arts
Mathematics

Grade(s)

9, 10, 11, 12

Overview

Is it possible to make a bad picture into a good picture with photo editing? When scientists enhance pictures from telescopes, are they really doing science, or are they just indulging their imaginations? Just how far can you zoom in to get information? When you're manipulating images, you have to be able to separate usable information from background noise.

This article will explain how photo editing software uses trigonometric identities and substitution to adjust the value of pixels in an image. There is a corresponding video and links to additional information.

English Language Arts (2021) Grade(s): 11

ELA21.11.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

UP:ELA21.11.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
English Language Arts (2021) Grade(s): 12

ELA21.12.8

Read, analyze, and evaluate texts from science, social studies, and other academic disciplines and explain how those disciplines treat domain-specific vocabulary and content and organize information.

UP:ELA21.12.8

Vocabulary

  • Academic disciplines
  • Domain-specific vocabulary
  • Content organization

Knowledge

Students know:
  • Strategies to read, analyze, and evaluate texts from various academic disciplines.
  • Content-specific text will often include a particular structure and domain-specific vocabulary.

Skills

Students are able to:
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine the use of domain-specific vocabulary.
  • Read, analyze, and evaluate texts from subjects other than English language arts to determine how the academic discipline organizes content.

Understanding

Students understand that:
  • Different academic disciplines may utilize different vocabulary.
  • Different academic disciplines may arrange content in particular organizational styles.
Mathematics (2019) Grade(s): 09-12 - Precalculus

MA19.PRE.37

Use trigonometric identities to solve problems.

UP:MA19.PRE.37

Vocabulary

  • Identity
  • Even and odd function
  • Sine
  • Cosine
  • Tangent
  • Cosecant
  • Secant
  • Cotangent
  • Fundamental Identities
  • Reciprocal Identities
  • Quotient Identities
  • Pythagorean Identities
  • Sum and Difference Identities
  • Double-Angle Identities
  • Half-Angle Identities

Knowledge

Students know:
  • Applications of the Pythagorean Theorem.
  • Operations with trigonometric ratios.
  • Operations with radians and degrees.
  • Even and odd functions.

Skills

Students are able to:
  • Use and transform the Pythagorean Identity.
  • Simplify trigonometric expressions.
  • Verify trigonometric identities.
  • Write the sum and difference identities for sine, cosine, and tangent.
  • Use sum and difference identities to findexact values of a trig function.
  • Derive the double angle and half angleidentities.

Understanding

Students understand that:
  • The fundamental identities allow functions to be written in terms of other functions. Then algebraic methods can be applied to simplify expressions or to match it with another expression
  • Given the trig values for a pair of angles, identities can be used to find the trig values of the sum or difference of the given angles.
  • Given the trig values for an angle, identities can be used to find the trig values for twice and half the angle.
ELA21.11.8
ELA21.12.8

CR Resource Type

Informational Material

Resource Provider

CK-12

License Type

Custom
https://www.ck12.org/c/calculus/trigonometric-substitution/rwa/Blurred-Lines/?r…

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/

Accessibility

Text Resources: Content is organized under headings and subheadings
Video resources: includes closed captioning or subtitles

Approved Date

Owner (Author)

habradley
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