Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. If there is no solution, enter NO SOLUTION.) 2 cos^2(𝜃) − cos(𝜃) − 1 = 0

Answer 1

2cos^2(T) - cosT -1 = 0

let x=cosT

2x^2 -x -1 = 0

factor

(2x+1)(x-1) = 0

set each factor = 0 and solve for x

2x+1=0, x =-1/2

x-1 = 0, x = 1

x=cosT

cosT = -1/2 or 1

T = (..., -2pi, -4pi/3, 0, 2pi/3, pi, 5pi/3, 2pi, 8pi/3, .... , 2kpi, 2pi/3+2kpi, ... ) where k= any integer

or theta = (120k, 360k) in degrees, where k = any integer, positive or negative

or theta = (2kpi, 2pi/3+2kpi) in radians were k = any integer

Answer 2

cos(θ) = 1 or cos(θ) = - 1/2;

θ = 2πk; θ = 2π/3 + 2kπ, θ = 4π/3 + 2kπ