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AP Calculus

This guide explores the unit circle and its relevance in defining trigonometric functions. It explains how to determine the sine and cosine values for angles in standard position, specifically 45 degrees, and emphasizes the concept of quadrantal angles that align with the axes. Additionally, it introduces trigonometric identities, which are fundamental relationships true for all defined variable values. The assignment includes practical exercises to simplify expressions using these identities, focusing on techniques like substitution and common denominators.

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AP Calculus

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  1. AP Calculus The Unit circle

  2. Def: If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ Trig functions defined using the unit circle are called circular functions.

  3. 1.) Find the exact values for the trig functions for 45o

  4. 2.) Find the exact values for the trig functions:

  5. Def: Quadrantal Angles:Angles whose terminal side coincides with either the x-axis or the y-axis are called quadrantal angles.

  6. A S T C- All Students Take Calculus!

  7. Def: Trigonometric Identities: The trigonometric identities are relationships which are true for all values of the variables for which the expressions are defined.

  8. 3. Use trig identities to simplify the following

  9. Suggestions • Change everything to sine and cosine • Substitute basic trig identities • Factor or foil the expression • Multiply both numerator and denominator by the same thing • Find a common denominator for sums and differences

  10. Assignment Practice Worksheet: Unit Circle

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