Solve $\cos (x)=0.11$ on $0 \leq x< 2 \pi$
There are two solutions, $A$ and $\mathrm{B}$, with $\mathrm{A}< \mathrm{B}$
\[
A=
\]
\[
B=
\]
Answer
The solutions to the equation \(\cos(x) = 0.11\) on \(0 \leq x < 2\pi\) are \(A = \boxed{1.46057327680715}\) and \(B = \boxed{4.8226120303724365}\)
Step 1 ：The cosine function, \(\cos(x)\), is equal to 0.11 at two points within the interval \(0 \leq x < 2\pi\). These points are the solutions to the equation.
Step 2 ：To find these points, we can use the arccosine function, \(\arccos(x)\), which gives the angle whose cosine is \(x\). However, the arccosine function only gives the angle in the first and second quadrants.
Step 3 ：To find the angle in the third and fourth quadrants, we subtract the result from \(2\pi\).
Step 4 ：Let's calculate the solutions: \(x = 0.11\)
Step 5 ：The first solution is \(A = 1.46057327680715\)
Step 6 ：The second solution is \(B = 4.8226120303724365\)
Step 7 ：The solutions to the equation \(\cos(x) = 0.11\) on \(0 \leq x < 2\pi\) are \(A = \boxed{1.46057327680715}\) and \(B = \boxed{4.8226120303724365}\)
