Trignometry Help Please?

Question

Solve 0 (degrees) less than or equal to x less or equal to 360 (degrees):

2cos^2 data - 5cos data +2 = 0

Answer 1

θ is called theta, not data. It's a Greek letter.

2cos^2(θ) - 5cos(θ) +2 = 0
Let u = cos(θ)

2u^2 - 5u + 2 = 0
Factor the quadratic:
(2u - 1)(u - 2) = 0

2u - 1 = 0
Add 1 to both sides:
2cos(θ) = 1
Divide both sides by 2:
cos(θ) = 1/2
Using the unit circle:
θ = π/3, 5π/3

u - 2 = 0
Add 2 to both sides:
cos(θ) = 2
Can't happen (range of cos(θ) is [-1,1])

θ = π/3, 5π/3

Answer 2

I think you mean "theta" rather than "data".

Theta is written as θ.

2cos²θ - 5cosθ + 2 = 0

Factor and treat cosθ like a variable x.

(2cosθ - 1)(cosθ - 2) = 0
cosθ = 1/2, 2

Since cosθ cannot equal 2 the only answer is:
cosθ = 1/2

θ = 60°, 300°

If you write it in radians rather than degrees, the answer is:

θ = π/3, 5π/3

Looks like Kyle beat me to the punch.

Answer 3

2cos^2(x) - 5cos(x) + 2 = 0

let y be cos(x)
2y^2 - 5y + 2 = 0

2y^2 - 1y - 4y + 2 = 0

(2y^2 - 1y) - (4y - 2) = 0

y(2y - 1) - 2(2y - 1) = 0

(2y - 1) (y - 2) = 0

y = 2 or 1/2

2 won't work because it's greater than 1

we know that y = cos(x)

1/2 = cos(x)
x = 60 degrees or 300 degrees