Find the Critical Points sin(x)

Problem

sin(x)

Solution

1. Identify the function ƒ(x)=sin(x) and recall that critical points occur where the first derivative is equal to zero or is undefined.

2. Differentiate the function with respect to x to find the first derivative.

d(sin(x))/d(x)=cos(x)

3. Set the derivative equal to zero to find the stationary points, noting that cos(x) is defined for all real numbers.

cos(x)=0

4. Solve for x by identifying the values where the cosine function equals zero.

x=π/2+n*π

5. Define the integer constant n to represent all possible solutions in the domain of real numbers.

n∈ℤ

Final Answer

x=π/2+n*π,n∈ℤ

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