cos(x)+0.45*sin(x)=0.9597?

Question

solve for the angle x and can u please include the steps

Answer 1

cos(x) = 0.9597 - 0.45*sin(x)
cos²(x) = (0.9597 - 0.45*sin(x))²
1 - sin²(x) = 0.922102409 - 0.86373 sin(x) + 0.2025 sin²(x)
0 = -0.07897591 - 0.86373 sin(x) + 1.2025 sin²(x)

sin(x) = [0.86373 ± √(0.86373² - 4*1.2025*(-0.07897591))]/2.405

sin(x) = .80033932 or sin(x) = -0.0820607

so x = 0.927861 or x = -0.0821531

or either of the above plus or minus an integer multiple of 2π

Answer 2

x = -0.08215311362
x = 0.9278609658
x = -5.355324341