PRECAL.MATH.5.M

Use trigonometric identities such as reciprocal, quotient, Pythagorean, cofunctions, even/odd, and sum and difference identities for cosine and sine to simplify trigonometric expressions.

Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
trigonometric identitiesreciprocal identitiesquotient identitiesPythagorean identitiescofunctionseven identitiesodd identitiessum and difference identitiescosinesinetrigonometric expressions
Skills
  • identify (reciprocal, quotient, Pythagorean, cofunction, even/odd, sum and difference identities) #dok1
  • apply (trigonometric identities to trigonometric expressions) #dok2
  • simplify (trigonometric expressions using identities) #dok2
  • use (sum and difference identities for cosine and sine) #dok2
  • select (appropriate identities to simplify trigonometric expressions) #dok3
Learning Targets
  • I can recognize and state the common trigonometric identities. #dok1
  • I can identify which identity to use for a given trigonometric expression. #dok1
  • I can apply reciprocal, quotient, and Pythagorean identities to rewrite trigonometric expressions. #dok2
  • I can simplify trigonometric expressions using cofunctions, even/odd, and sum and difference identities. #dok2
  • I can select and justify the use of specific identities to simplify complex trigonometric expressions. #dok3
  • I can explain my reasoning for each step in simplifying a trigonometric expression using various identities. #dok3
Big Ideas
  • Trigonometric identities are mathematical tools that allow for the simplification and transformation of trigonometric expressions.
  • Mastering a variety of trigonometric identities enables students to solve complex equations and model real-world phenomena more effectively.
Essential Questions
  • How do different trigonometric identities help to simplify complex trigonometric expressions?
  • When is it more efficient to use one identity over another?
  • How do the even and odd properties of trigonometric functions affect the simplification process?
  • Why is it important to justify the steps taken when simplifying trigonometric expressions?
  • How can sum and difference identities for cosine and sine be applied to solve real-world problems?