= 2.1532 + 2kπ or = 2π 2.1532 + 2kπ, for k Z. x x – Since 0 2π, there are two answers, = 2.1532 and = 2π - 2.1532 = 4.13. x< x x ≤ 31. cos (x) = 0.71 = cos-1 (0.71) x = 0.7813 + 2kπ or = 2π 0.7813 + 2kπ, for k Z. x x – Since 0 2π, there are two answers, = 0.7813 or = 2π 0.7813 = 5.5019. x< x x ≤ – 33. 7sin (6x) = 2 sin () = 6x = sin-1 () 6x = 0.28975 + 2kπ or 6x = 0.28975 + 2kπ, for k Z. π – In order to get the first two positive solutions, k = 0. This leads to: 6x = 0.28975 or 6x = 0.28975 = 2.85184 π – = 0.04829 or = 0.47531 x x 35.5cos (3x) = cos (3x) = 3x = cos-1 ( 3x = 2.2143 + 2kπ or 3x = 2π 2.2143 + 2kπ, for k Z. – In to get the first two positive solutions, k = 0. This leads to: 3x = 2.2143 or 3x = 2π 2.2143 = 4.0689 – = 0.7381 or = 1.3563 x x 37. 3sin () = sin () = = sin-1 ( = 0.72973 + 2kπ or = 0.72973 + 2kπ, for k Z. π – In order to get the first two positive solutions, k = 0. This leads to: = 0.72973 or = 0.72973 = 2.41186 π – = 0.9291 or = 3.0709 39. 5cos () = cos () =
x = 2.1532 + 2kπ or x = 2π – 2.1532 + 2kπ, for k Z. Since 0 ≤ x< 2π, there are two answers, x = 2.1532 and x = 2π - 2.1532 = 4.13. 31. cos (x) = 0.71 x = cos-1 (0.71) x = 0.7813 + 2kπ or x = 2π – 0.7813 + 2kπ, for k Z. Since 0 ≤ x< 2π, there are two answers, x = 0.7813 or x = 2π – 0.7813 = 5.5019. 33. 7sin (6x) = 2 sin () = 6x = sin-1 () 6x = 0.28975 + 2kπ or 6x = π – 0.28975 + 2kπ, for k Z. In order to get the first two positive solutions, k = 0. This leads to: 6x = 0.28975 or 6x = π – 0.28975 = 2.85184 x = 0.04829 or x = 0.47531 35.5cos (3x) = cos (3x) = 3x = cos-1 ( 3x = 2.2143 + 2kπ or 3x = 2π – 2.2143 + 2kπ, for k Z. In to get the first two positive solutions, k = 0. This leads to: 3x = 2.2143 or 3x = 2π – 2.2143 = 4.0689 x = 0.7381 or x = 1.3563 37. 3sin () = sin () = = sin-1 ( = 0.72973 + 2kπ or = π – 0.72973 + 2kπ, for k Z. In order to get the first two positive solutions, k = 0. This leads to: = 0.72973 or = π – 0.72973 = 2.41186 = 0.9291 or = 3.0709 39. 5cos () = cos () =
Chapter%206%20Solutions.docx