Give the solutions to the equation (sin x − 1)(3cos x + 2) = 0 in [0, 2π]. Enter solutions in order from least to greatest. Round approximate solutions to three decimal places.

Question

I have x = 2.301 and x = 3.983 that are both right. x = 1 and x = pi + 1 both did not work and were wrong. I cannot find the solution that goes first. Please help, thank you!

Answer 1

(sin x - 1)(3 cos x + 2) = 0

By Zero Product Rule

sin x - 1 = 0

sin x = 1

x = π / 2

x = 1.57

or

3 cos x + 2 = 0

3 cos x = -2

cos x = -2 / 3

arccos -2/3 = 2.300