Eco_Explorer
Eco_Explorer 1d ago • 0 views

Illustrative Examples for Antiderivatives of Trigonometric Functions

Hey there, math enthusiasts! 👋 Let's conquer antiderivatives of trigonometric functions together. This guide will help you understand the basics and test your knowledge with a fun quiz! 🧮
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debra511 Jan 2, 2026

📚 Quick Study Guide

  • 📐 The antiderivative of $\sin(x)$ is $-\cos(x) + C$. Remember the negative sign!
  • 🧭 The antiderivative of $\cos(x)$ is $\sin(x) + C$. No negative sign here.
  • 📈 The antiderivative of $\sec^2(x)$ is $\tan(x) + C$. This is a common one.
  • 🔗 The antiderivative of $\csc^2(x)$ is $-\cot(x) + C$. Watch out for the negative.
  • 💡 The antiderivative of $\sec(x)\tan(x)$ is $\sec(x) + C$.
  • 🧪 The antiderivative of $\csc(x)\cot(x)$ is $-\csc(x) + C$. Negative again!
  • 📝 Remember the constant of integration, $C$, for all indefinite integrals.
  • ➕ Don't forget u-substitution can be your best friend for more complex problems.

Practice Quiz

  1. What is the antiderivative of $\sin(x)$?
    1. $\cos(x) + C$
    2. $-\cos(x) + C$
    3. $\sec(x) + C$
    4. $-\sec(x) + C$
  2. What is the antiderivative of $\cos(x)$?
    1. $\sin(x) + C$
    2. $-\sin(x) + C$
    3. $\tan(x) + C$
    4. $-\tan(x) + C$
  3. What is the antiderivative of $\sec^2(x)$?
    1. $\tan(x) + C$
    2. $\cot(x) + C$
    3. $\sec(x) + C$
    4. $\csc(x) + C$
  4. What is the antiderivative of $\csc^2(x)$?
    1. $\tan(x) + C$
    2. $-\cot(x) + C$
    3. $\sec(x) + C$
    4. $-\csc(x) + C$
  5. What is the antiderivative of $\sec(x)\tan(x)$?
    1. $\sec(x) + C$
    2. $\tan(x) + C$
    3. $\csc(x) + C$
    4. $\cot(x) + C$
  6. What is the antiderivative of $\csc(x)\cot(x)$?
    1. $\sec(x) + C$
    2. $-\csc(x) + C$
    3. $\csc(x) + C$
    4. $-\cot(x) + C$
  7. What is the antiderivative of $2\sin(x)$?
    1. $2\cos(x) + C$
    2. $-2\cos(x) + C$
    3. $\cos(2x) + C$
    4. $-\cos(2x) + C$
Click to see Answers
  1. B
  2. A
  3. A
  4. B
  5. A
  6. B
  7. B

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