Determine solutions for each equation in the interval 0 ≤ x ≤ 2π, to the nearest hundredth of a radian.
Give exact answers where possible.
a) sin x − 0.8 = 0
To solve the equation sin x - 0.8 = 0, we can first isolate the sine term by adding 0.8 to both sides:
sin x = 0.8
To find the solutions within the given interval 0 ≤ x ≤ 2π, we can use the inverse sine function or arcsine function (sin^(-1)).
x = sin^(-1)(0.8)
Using a calculator, we find the arcsine of 0.8 is approximately 0.9273 radians.
Therefore, the solution for the equation sin x - 0.8 = 0 in the interval 0 ≤ x ≤ 2π is x = 0.93 radians (to the nearest hundredth of a radian).