Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Trig equation

Solve for θ in the interval -180≤θ≤180.

cosθ (cosθ - 2) = 1

Thanks.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Trig equation

cosθ(cosθ-2) = 1
cos²θ - 2cosθ - 1 = 0

Let y = cosθ. Then y² - 2y - 1 = 0.

Solving this quadratic gives that y = 1±√2.

Therefore, cosθ = 1±√2.
But -1≤cosθ≤1 for all θ, so therefore cosθ = 1-√2.

Using a calculator, cos[sup]-1[/sup](1-√2) ≈114.5°.
But cosθ = cos(-θ), so -114.5° is also a solution.

Therefore, θ ≈ ± 114.5°.

I'm not sure if there's a purely trigonometric way of doing it though.

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