Find all solutions to the equation 11 cos x=frac{1}{cos x} for 0 leq x leq 2 pi. Enter your answers in increasing order, rounded to three decimal places.

Question

Accepted Answer

Step:1 ：Given the equation (11 cos x=frac{1}{cos x}). This can be rewritten as (11 cos^2 x = 1).Step:2 ：Solving for (cos x), we get (cos x = pm frac{1}{sqrt{11}}).Step:3 ：We need to find the values of (x) in the interval ([0, 2pi]) that satisfy this equation.Step:4 ：The solutions to the equation are approximately (x = 1.265, 1.877, 4.406, 5.019).Step:5 ：Final Answer: The solutions to the equation (11 cos x=frac{1}{cos x}) for (0 leq x leq 2 pi) are (boxed{1.265, 1.877, 4.406, 5.019}).

Answer

Step: 1 ：Given the equation (11 cos x=frac{1}{cos x}). This can be rewritten as (11 cos^2 x = 1).Step: 2 ：Solving for (cos x), we get (cos x = pm frac{1}{sqrt{11}}).Step: 3 ：We need to find the values of (x) in the interval ([0, 2pi]) that satisfy this equation.Step: 4 ：The solutions to the equation are approximately (x = 1.265, 1.877, 4.406, 5.019).Step: 5 ：Final Answer: The solutions to the equation (11 cos x=frac{1}{cos x}) for (0 leq x leq 2 pi) are (boxed{1.265, 1.877, 4.406, 5.019}).

Find all solutions to the equation $11 \cos x = \frac{1}{\cos x}$ for $0 \leq x \leq 2 π$ . Enter your answers in increasing order, rounded to three decimal places.

Answer

Popular Problems

Find all solutions to the equation 11cos⁡x=1cos⁡x for 0≤x≤2π. Enter your answers in increasing order, rounded to three decimal places.

Answer

Popular Problems

Find all solutions to the equation $11 \cos x = \frac{1}{\cos x}$ for $0 \leq x \leq 2 π$ . Enter your answers in increasing order, rounded to three decimal places.