Use inverse trigonometric functions to find a solution to the equation in the given interval. Then, use a graph to find all other solutions to the equation on this interval.
\[
\cos x=-0.55,0 \leq \theta \leq 2 \pi
\]
Enter your answers in increasing order. Round your answers to two decimal places.
Answer
The solutions to the equation \(\cos x=-0.55\) in the interval \(0 \leq \theta \leq 2 \pi\) are \(\boxed{123.37}\) and \(\boxed{236.63}\) degrees.
Step 1 ：The cosine function is negative in the second and third quadrants. So, we need to find the reference angle in the first quadrant and then find the angles in the second and third quadrants.
Step 2 ：We can use the arccos function to find the reference angle. The reference angle is \(\arccos(-0.55) = 0.9884320889261531\) radians.
Step 3 ：Then, we can subtract this angle from \(\pi\) to find the angle in the second quadrant and add it to \(\pi\) to find the angle in the third quadrant. We need to make sure that the angles are in the given interval [0, 2\(\pi\)].
Step 4 ：The angle in the second quadrant is \(\pi - 0.9884320889261531 = 123.37\) degrees.
Step 5 ：The angle in the third quadrant is \(\pi + 0.9884320889261531 = 236.63\) degrees.
Step 6 ：The solutions to the equation \(\cos x=-0.55\) in the interval \(0 \leq \theta \leq 2 \pi\) are \(\boxed{123.37}\) and \(\boxed{236.63}\) degrees.
