Question

Find all solutions in radians. Approximate your answers to the nearest hundredth. (Let k be any integer.)

cos (2x − 1) = 0.9
x=

Answer 1

Answer: 0.73 + πk, 0.28 + πk

Step-by-step explanation:

cos (2x - 1) = 0.9

cos⁻¹[cos (2x - 1)] = cos⁻¹ 0.9

2x - 1 = +/- 0.45

2x = +/- 0.45 + 1

x =
`(+/- 0.45 + 1)/(2)`

x =
`(0.45 + 1)/(2)`, x =
`(-0.45 + 1)/(2)`

x = 0.73, 0.28

For ALL Solutions:

x = 0.73 + πk and x = 0.28 + πk