Find all solutions of the equation in the interval 0 2 algeb

Find all solutions of the equation in the interval [0, 2) algebraically. Use the table feature of a graphing utility to check your answers numerically. (Write your answers in terms of . Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

x =
x =
x =
x =

Solution

sin²x + cosx + 1 = 0

(1 - cos²x) + cos x + 1 = 0

cos²x - cos x - 2 = 0

(cosx - 2)(cosx + 1) = 0

cosx = 2 =======> not possible

cosx = -1 =======> x =