Solve 2cos^2x + cosx - 1 = 0 for x over the interval [0, 2 π).

a.π and π/3

b.π, π/3, and 5π/3

c. 1 and 2π/3

d. 1, 2π/3, and 4π/3

e. 1, π/3, and 5π/3

Question

Mathematics

Demarcus Cuevas

30 November, 12:00

Solve 2cos^2x + cosx - 1 = 0 for x over the interval [0, 2 π).

a.π and π/3

b.π, π/3, and 5π/3

c. 1 and 2π/3

d. 1, 2π/3, and 4π/3

e. 1, π/3, and 5π/3

+2

Answers (1)

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Chaos · Answer 1

Let cos x = a, then

2a^2 + a - 1 = 0,

solving the quadratic equation, we have:

a = 0.5 or - 1.

i. e. cos x = 0.5 or cos x = - 1

for cos x = 0.5,

x = pi/3, 2pi - pi/3 = pi/3, 5pi/3

for cos x = - 1,

x = pi

therefore, x = pi, pi/3, 5pi/3

Answer: B

Solve 2cos^2x + cosx - 1 = 0 for x over the interval [0, 2 π).a.π and π/3b.π, π/3, and 5π/3c. 1 and 2π/3d. 1, 2π/3, and 4π/3e. 1, π/3, and 5π/3

Solve 2cos^2x + cosx - 1 = 0 for x over the interval [0, 2 π).

a.π and π/3

b.π, π/3, and 5π/3

c. 1 and 2π/3

d. 1, 2π/3, and 4π/3

e. 1, π/3, and 5π/3