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Trig Derivatives Flashcards

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Description

This interactive flashcard MicroSim helps students memorize the derivatives of all six trigonometric functions:

Function Derivative
sin(x) cos(x)
cos(x) -sin(x)
tan(x) sec²(x)
cot(x) -csc²(x)
sec(x) sec(x)tan(x)
csc(x) -csc(x)cot(x)

The cards are arranged in pairs that share related patterns:

  • Pair 1: sin/cos (co-functions)
  • Pair 2: tan/cot (tangent family)
  • Pair 3: sec/csc (secant family)

Color Coding

  • Blue background: Derivatives that are positive
  • Red background: Derivatives that are negative (contain a minus sign)

This color pattern helps students remember the important rule: "co-functions have negative derivatives" (cos, cot, csc all have negative signs in their derivatives).

Interactive Features

  • Click to flip: Click any card to reveal its derivative
  • Quiz Mode: Test yourself by typing the derivative before seeing the answer
  • Show All / Hide All: Quickly reveal or hide all derivatives
  • Focus dropdown: Select a specific function to study in isolation

Lesson Plan

Learning Objective

Students will recall the derivatives of all six trigonometric functions (Bloom Level 1: Remember).

Grade Level

High School AP Calculus, College Calculus I

Duration

10-15 minutes for initial practice, then 5 minutes daily for reinforcement

Prerequisites

  • Understanding of trigonometric functions
  • Basic concept of derivatives

Activities

Activity 1: Introduction (5 minutes)

  1. Click through each card to see all six derivatives
  2. Notice the patterns:
  3. sin and cos are derivatives of each other (with sign change)
  4. tan and sec are related (sec appears in both)
  5. cot and csc are related (csc appears in both)
  6. Observe the color coding: negative derivatives are on red cards

Activity 2: Pattern Recognition (5 minutes)

  1. Use the "Show All" button to display all derivatives
  2. Discuss with students:
  3. Why do co-functions have negative derivatives?
  4. What patterns do you notice in the secant/cosecant derivatives?
  5. Use the focus dropdown to isolate each pair

Activity 3: Quiz Practice (10 minutes)

  1. Click "Quiz Mode" to enter testing mode
  2. Click a card to select it for testing
  3. Type your answer and press Enter
  4. Track your score and repeat until mastery

Activity 4: Daily Practice (5 minutes daily)

  1. Open the MicroSim at the start of class
  2. Complete one round of quiz mode
  3. Aim for 6/6 correct within 30 seconds

Assessment

  • Formative: Quiz mode score tracking
  • Summative: Timed quiz - identify all 6 derivatives in under 30 seconds

Memory Tips to Share

  1. "Negative co-" rule: cos, cot, csc all start with "co-" and all have negative derivatives
  2. sec/tan pattern: sec(x) derivative contains both sec and tan; tan(x) derivative is sec²
  3. csc/cot pattern: csc(x) derivative contains both csc and cot; cot(x) derivative is -csc²

Delta Moment

"These six derivatives are like a family! Once you see the patterns, you will never forget them. The 'co-' functions are the grumpy ones - they always bring a negative sign to the party."

References