Solve for x cos(x)=0

Problem

cos(x)=0

Solution

1. Identify the values on the unit circle where the x-coordinate is zero.

2. Determine the primary angles within the interval [0,2*π) that satisfy the equation.

3. Find the first solution:

cos(x)=0⇒x=π/2

4. Find the second solution:

cos(x)=0⇒x=(3*π)/2

5. Generalize the solution to include all possible rotations by adding multiples of π since the zeros of the cosine function occur every π radians.

x=π/2+n*π

Final Answer

cos(x)=0⇒x=π/2+n*π,n∈ℤ

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