Solve for the exact solutions in the interval [0,2π). Separate solutions with a comma.If the equation has no solutions, respond with DNE.

Question

Solve for the exact solutions in the interval . Separate solutions with a comma.If the equation has no solutions, respond with DNE.

sin(5x)= - 1/2

Answer 1

sin(pi/6) = 1/2

5x = pi/6 or 5pi/6 + 2npi where n = any integer

x = pi/30 or pi/6 + 2npi/5 where n = any integer

sin(30 degrees) = 1/2 (this came up in one of the earliest Big Bang Theory TV shows, where Sheldon and Leonard try to move Penny's new package up the stairs, as they contemplate force needed to move it up a 30 degree incline. Lenoard says the sin30 is about 1/2. Sheldon says "exactly 1/2" Leonard is offended as he mimics Sheldon in a disparaging voice "Exactly a half")

30/5= 6 degrees=x