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
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