Integrals Using Trigonometric Substitutions

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

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.  

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.

CR Resource Type

Informational Material

Resource Provider

CK-12

License Type

Custom

Accessibility

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