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### Course: AP®︎/College Calculus AB>Unit 2

Lesson 8: Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)

# Derivatives of sin(x) and cos(x)

Now we explore the intuition behind the derivatives of trigonometric functions, discovering that the derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). By analyzing tangent line slopes, we gain a deeper understanding of these fundamental relationships.

## Want to join the conversation?

• Regarding the unit circle, when sin is 0 cos is 1 or -1. But sin's slope will be 0/ infinity or 0/ - infinity. Both undefined and not cos. Not sure what im doing wrong here.
• Remember, a derivative involves instantaneous slope, but that doesn't mean that you're dividing by zero - if so, then we couldn't take the derivative of any function! You should try reviewing the videos on derivatives to get a feel for the intuition of what instantaneous slope really means.
• At which points are the tangents of cos x and sin x parallel ? What makes them important ?