Question

what does cos x = 0.418? On the interval (0,2pi)

Answer 1

set your calculator to RAD , enter

2ndF (or similar key)
cos
.418
=
to get 1.13955 radians , which would be your quadrant I angle.
but the cosine is also positive in quad IV
so x = 1.13955 or x = 2π - 1.13955 = 5.14363