Solve for x cos(x)=3/4

Problem

cos(x)=3/4

Solution

1. Identify the equation as a basic trigonometric equation where you need to find the angle x whose cosine is 3/4

2. Apply the inverse cosine function to both sides of the equation to isolate x

arccos(cos(x))=arccos(3/4)

3. Determine the general solution for x by considering the periodicity of the cosine function (2*π*n and its symmetry across the x-axis (±.

x=±arccos(3/4)+2*π*n

4. Specify the integer constraint where n represents any integer.

n∈ℤ

Final Answer

cos(x)=3/4⇒x=±arccos(3/4)+2*π*n,n∈ℤ

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