Solve for x sin(x)cos(x)=0

Problem

sin(x)*cos(x)=0

Solution

1. Apply the Zero Product Property to the equation, which states that if the product of two factors is zero, at least one of the factors must be zero.

sin(x)=0

cos(x)=0

2. Solve the first equation for x by identifying where the sine function equals zero on the unit circle.

sin(x)=0⇒x=n*π

where *n* is any integer.

3. Solve the second equation for x by identifying where the cosine function equals zero on the unit circle.

cos(x)=0⇒x=π/2+n*π

where *n* is any integer.

4. Combine the solutions into a single expression. The values 0,π/2,π,(3*π)/2,… occur at every multiple of π/2

x=(n*π)/2

Final Answer

sin(x)*cos(x)=0⇒x=(n*π)/2

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