Question

Question #3efc5

Answer 1

`θ = 90°`, or `180°`, or `270°`.

Explanation:

First, we can factor our a `4cosθ` to get:

`4cosθ(cosθ + 1) = 0`

This means that either `4cosθ = 0 => cosθ = 0`

or `cosθ + 1 = 0 => cosθ = -1`

You can consult the trigonometric circle below to help:

graph{x^2 +y^2 = 1 [-2.5, 2.5, -1.25, 1.25]}

`cosθ` corresponds to the `x` axis. The angle `θ` is measured from the Ox semiaxis, going counterclockwise. Therefore,

`cosθ = 0 => θ = 90°` or `θ = 270°`
`cosθ = -1 => θ = 180°`

So the three possible solutions are

`{90°, 180°, 270°}`

Answer 2

`theta = 90^o, 180^o and 270^o`

Explanation:

Factor: `4cos theta (cos theta + 1) = 0`

`4 cos theta = 0, and cos theta = -1`

From a trig. circle: `cos theta = 0` occurs at `90^o and 270^o`
From a trig. circle: `cos theta = -1` occurs at `180^o`