Use the Quadratic Formula to find all solutions of the equation in the interval [0, 2𝜋).

Question

Use the Quadratic Formula to find all solutions of the equation in the interval [0, 2𝜋). (Enter your answers as a comma-separated list. Round each answer to four decimal places.)

15 sin²(x) − 22 sin(x) + 8 = 0

x=

Answer 1

Using the quadratic formula, sin x = 4/5 and sin x = 2/3 are the two solutions.

sin^-1 (4/5) = 0.9273 That is one solution. Sin xπ is also positive in Quad 2. (π - 0.9273) = 2.2143 is the 2nd solution.

sin^-1 (2/3) = 0.7297 (π - 0.7297) = 2.4119

The solyutions are x = .7297, .9273, 2.2143, and 2.4119