Solve for x cos(x)=3/4

Problem

cos(x)=3/4

Solution

1. Identify the equation as a basic trigonometric equation of the form cos(x)=a where a=3/4

2. Apply the inverse cosine function to find the principal value, often called the arccosine.

x=arccos(3/4)

3. Account for symmetry of the cosine function on the unit circle. Since cos(x)=cos(−x) the solutions within one period [0,2*π) are x=arccos(3/4) and x=2*π−arccos(3/4)

4. Generalize the solution by adding integer multiples of the period 2*π to include all possible angles in the domain of real numbers.

x=±arccos(3/4)+2*π*n

Final Answer

cos(x)=3/4⇒x=±arccos(3/4)+2*π*n,n∈ℤ

Want more problems? Check here!