MA19.PRE.37

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

MA19.PRE.37
Use trigonometric identities to solve problems.

Unpacked Content

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.

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

Aligned Learning Resources

Integrals Using Trigonometric Substitutions

Integrals: Trigonometric Substitution Video

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