please help thanks so much

Question

Use a graphing utility to approximate the solutions of the equation in the interval [0, 2𝜋) by collecting all terms on one side, graphing the new equation, and using the zero or root feature to approximate the x-intercepts of the graph. (Round your answers to four decimal places.

3 sin(x) = cos(x) − 2

Answer 1

3 sin(x) = cos(x) − 2

To collect all terms on one side, subtract cos(x) and add 2 to both sides. Then we will have

y = 3 sin(x) - cos(x) + 2

Graphing this and marking the zeros (where the curve crosses the x axis) gives us the graph seen below...

The zeros are 4.148 and 5.920

And they repeat again at 10.431 and 12.203

(The zeros repeat every 6.283 in both directions, which is 2 x 3.1415 or 2π)

So your final answer is 4.148 ± 2π and 5.920 ± 2π