Solve for x cos(x)=3/5

Problem

cos(x)=3/5

Solution

1. Identify the equation as a basic trigonometric equation where you need to find the angle x whose cosine is 3/5

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

x=arccos(3/5)

3. Determine the general solution by considering the periodicity of the cosine function, which repeats every 2*π radians, and its symmetry across the x-axis (cos(x)=cos(−x).

x=±arccos(3/5)+2*π*n

4. State the constraint for the integer n which represents any integer rotation.

n∈ℤ

Final Answer

cos(x)=3/5⇒x=±arccos(3/5)+2*π*n

Want more problems? Check here!