F-TF - Domain

Trigonometric Functions

High School Functions · Common Core State Standards · Common Core 2010

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Vocabulary
radian measureanglearcunit circlecoordinate planetrigonometric functionsreal numbersspecial trianglessinecosinetangentsymmetryperiodicitytrigonometric identitiesPythagorean identityquadrant
Skills
  • Understand (radian measure of an angle) #dok1
  • Identify (unit circle and arc length) #dok1
  • Recognize (special angles: π/3, π/4, π/6) #dok1
  • Explain (unit circle enabling extension of trigonometric functions) #dok2
  • Determine (geometric values of sine, cosine, and tangent) #dok2
  • Use (unit circle for symmetry and periodicity) #dok2
  • Model (periodic phenomena using trigonometric functions) #dok3
  • Solve (trigonometric equations in modeling contexts) #dok3
  • Prove (trigonometric identities and formulas) #dok4
Learning Targets
  • I can understand the radian measure of an angle as the length of the arc on the unit circle. #dok1
  • I can identify special angles such as π/3, π/4, and π/6. #dok1
  • I can explain how the unit circle allows the extension of trigonometric functions to all real numbers. #dok2
  • I can determine the values of sine, cosine, and tangent using special triangles. #dok2
  • I can model periodic phenomena using trigonometric functions with specified amplitude and frequency. #dok3
  • I can solve trigonometric equations in modeling contexts. #dok3
  • I can prove trigonometric identities, including the Pythagorean identity and addition/subtraction formulas. #dok4
Big Ideas
  • The unit circle plays a crucial role in extending trigonometric functions beyond specific angles, enhancing our ability to analyze periodic phenomena.
  • Proving and applying trigonometric identities deepen the understanding of mathematical relationships and improve problem-solving skills in various contexts.
Essential Questions
  • What is radian measure, and how is it related to the unit circle?
  • How does the unit circle help in extending trigonometric functions to all real numbers?
  • Can you explain the geometric significance of special angles like π/3, π/4, and π/6 in trigonometric functions?
  • How can trigonometric functions be applied to model real-world periodic phenomena?
  • What role do trigonometric identities play in solving advanced mathematical problems?