ALEX Classroom Resources

ALEX Classroom Resources  
   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 37 :
37. Use trigonometric identities to solve problems.

a. Use the Pythagorean identity sin2 (θ) + cos2(θ) = 1 to derive the other forms of the identity.

Example: 1 + cot2 (θ) = csc2 (θ)

b. Use the angle sum formulas for sine, cosine, and tangent to derive the double angle formulas.

c. Use the Pythagorean and double angle identities to prove other simple identities.
Subject: Mathematics (9 - 12)
Title: Integrals Using Trigonometric Substitutions
URL: https://www.ck12.org/c/calculus/trigonometric-substitution/lesson/Integrals-Using-Trigonometric-Substitutions-CALC/?referrer=concept_details
Description:

This informational material will explain how to solve problems using trigonometric identities by using trigonometric substitution. There are corresponding videos available. Practice questions with a PDF answer key are provided.  


   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 37 :
37. Use trigonometric identities to solve problems.

a. Use the Pythagorean identity sin2 (θ) + cos2(θ) = 1 to derive the other forms of the identity.

Example: 1 + cot2 (θ) = csc2 (θ)

b. Use the angle sum formulas for sine, cosine, and tangent to derive the double angle formulas.

c. Use the Pythagorean and double angle identities to prove other simple identities.
Subject: Mathematics (9 - 12)
Title: Integrals: Trigonometric Substitution Video
URL: https://www.ck12.org/c/calculus/trigonometric-substitution/lecture/Integrals:-Trigonometric-Substitution/?referrer=concept_details
Description:

This Khan Academy video on the CK-12 website will demonstrate how to solve problems using trigonometric identities with substitution.


   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 37 :
37. Use trigonometric identities to solve problems.

a. Use the Pythagorean identity sin2 (θ) + cos2(θ) = 1 to derive the other forms of the identity.

Example: 1 + cot2 (θ) = csc2 (θ)

b. Use the angle sum formulas for sine, cosine, and tangent to derive the double angle formulas.

c. Use the Pythagorean and double angle identities to prove other simple identities.
[ELA2021] (11) 8 :
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.
[ELA2021] (12) 8 :
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.
Subject: Mathematics (9 - 12), English Language Arts (11 - 12)
Title: Blurred Lines
URL: https://www.ck12.org/c/calculus/trigonometric-substitution/rwa/Blurred-Lines/?referrer=concept_details
Description:

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.


ALEX Classroom Resources: 3

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