Use a graphing utility to approximate (to three decimal places) the solutions of the equation in the interval [0, 2𝜋). (Enter your answers as a comma-separated list.) csc2(x) − 5 = 0

Question

Use a graphing utility to approximate (to three decimal places) the solutions of the equation in the interval [0, 2𝜋). (Enter your answers as a comma-separated list.)

csc²(x) − 5 = 0 

x=

Answer 1

csc²x = 5; cot²x = 4; cotx = ±2; tanx = ±1/2;

tanx= 1/2; x = tan^-1(1/2) = 0.464 or x = tan^-1(1/2) + π = 3.605

tanx = - 1/2; x = - tan(1/2) + π = 2.678 or x = - tan^-1(1/2) + 2π = 5.820