exact solution for: 2 Cos X + 1 = 0?

Answer 1

cos x = - 1/2 (2nd and 3rd quadrants)
x = 120 ° , 240 °

Answer 2

This simplifies to cos(x) = -1/2. So if we restrict the range of x to be between 0 and 2π, x = 2π/3 or 4π/3 (or in degrees, 120 and 240).

So there's more than one solution, not one single "exact" solution. If you want the full range of solutions, you could say the solutions are were we have π/3 in the third or fourth quadrant, so it's an odd mulitple of π plus or minus π/3. This means you can rewrite it as (2n+1)π + π/3, which becomes (6n+3 ± 1)π/3. Actually, in this case you can consider negative angles too so the full answer is ±(6n+3 ± 1)π/3 where n = 0, 1, 2, 3, 4...

Answer 3

2 Cos X + 1 = 0

2 cos X = -1

cos X = -1/2

X = cos ^-1(-1/2)

X = 120

Answer 4

sin 2x + sqrt(2) cos x = 0 or 2 sin x cos x + cos x sqrt(2) = 0 so cos x = 0 (it is x = pi/2+2npi or 3pi/2 +2npi) or 2 sin x + sqrt(2) = 0 sin x = - sqrt(2)/2 x = -pi/4 or 5pi/4 or 2npi further to them if co

Answer 5

cos x = -1/2

Note that cos (4Pi/3) =-1/2

cos x = cos(4Pi/3)

x = 4Pi/3 ( when x is between 0 and 2Pi)

Answer 6

cosX = -1/2
X = 2pi/3, 4pi/3
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Ideas: cosX is negative in the second and third quadrants.