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Derivatives of Trig Functions Calculator

Trig derivative calculator for sin, cos, tan, cot, sec, csc. Enter x in radians to get the derivative formula and value—great for trigonometric differentiation.

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(sin x)′=cos x (cos x)′=−sin x (tan x)′=sec²x
Trig function
e.g. π/3≈1.047

📖 Tutorial｜Derivatives of Trig Functions

1. Definition
Derivatives: sin→cos, cos→−sin, tan→sec², cot→−csc², sec→sec·tan, csc→−csc·cot.
2. Symbols
FunctionDerivative
sin xcos x
cos x−sin x
tan xsec²x
cot x−csc²x
sec xsec x tan x
csc x−csc x cot x
3. How it works
  • We apply the analytic formula for the chosen function;
  • x is in radians;
  • Then substitute x.
4. Steps
  1. Choose a trig function;
  2. Enter x in radians;
  3. Click Calculate.
5. Example
Example: sin x at x=π/3. (sin x)′=cos x=0.5.
6. Pitfalls
cos carries a minus sign;
x must be in radians, not degrees;
tan and cot are undefined at ±π/2.

❓ FAQ｜Derivatives of Trig Functions

Why does (cos x)′ carry a minus?
It follows from the important limits and definition; cos′=−sin, unlike sin.
How to remember sec and csc?
sec′=sec·tan; csc′=−csc·cot; the “co” ones add a minus.
Why must x be in radians?
(sin x)′=cos x holds only in radians; degrees add a π/180 factor.
Is tan′ sec² or 1/cos²?
They are equal: sec²x=1/cos²x.
What is cot's derivative?
(cot x)′=−csc²x=−1/sin²x.