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Exploring Derivatives of Trigonometric Functions with Graphs

Learn how to find derivatives of trig functions using graphs to visualize slope changes and curve patterns. Explore cosine and sine curves and apply the quotient rule for tangent derivatives. Adapted from Greg Kelly's teachings at Hanford High School in Richland, Washington.

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Exploring Derivatives of Trigonometric Functions with Graphs

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  1. Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon Siena College Photo by Vickie Kelly, 2001 Derivatives of Trig Functions London Bridge, Lake Havasu City, Arizona

  2. slope Consider the function We could make a graph of the slope: Now we connect the dots! The resulting curve is a cosine curve.

  3. slope We can do the same thing for The resulting curve is a sine curve that has been reflected about the x-axis.

  4. We can find the derivative of tangent x by using the quotient rule.

  5. Derivatives of the remaining trig functions can be determined the same way. p

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