Which of the following the set of all values of x such that 0≤x≤2pi and cos x = -1/2?

Question

{ π/6 , 5π/6 }

{π/3 , 5π/6 }

{π/2 , 3π/2 }

{2π/3 , 4π/3 }

{2π/3 , 5π/3 }

Answer 1

cosx = -1/2
the angel with 1/2 is angle 60 or pi/3
but -1/2 so this angel will be in the second (180-60= 120) and third quarant (180+60 = 240)
so that is 120 degree = 120pi/180 = 2pi/3 and 240 degree = 240pi/180 = 4pi/3
so answer will be {2π/3 , 4π/3 }

Answer 2

The easiest way to look at this is to visualize (or just draw) a circle in the x-y plane, with the center at the origin. Imagine it is of radius 1 unit. Your positive x axis is zero degrees, and if you sweep through the circle you get to 360 degrees.

Your x axis value is -0.5 (that is the definition of cosine). By visualizing or drawing it you can see that your answer is 90 + 30, or 270 - 30. Convert that to radians and you have the answer.

Answer 3

none of these, the set is 2pi/3, 11pi/6