Learning Resource Type

Classroom Resource

Integrals: Trigonometric Substitution Video

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

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

    Mathematics (2019) Grade(s): 09-12 - Precalculus

    MA19.PRE.37

    Use trigonometric identities to solve problems.

    Unpacked Content

    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.
    Link to Resource

    CR Resource Type

    Audio/Video

    Resource Provider

    CK-12
    Accessibility

    Accessibility

    Video resources: includes closed captioning or subtitles
    License

    License Type

    Custom
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