Statement Solve for 0∘≤θ≤360∘0^\circ\le\theta\le 360^\circ0∘≤θ≤360∘: 2cos2θ−3cosθ+1=0.2\cos^2\theta-3\cos\theta+1=0.2cos2θ−3cosθ+1=0. Solution Putting c=cosθc=\cos\thetac=cosθ: 2c2−3c+1=0⇒c=3±9−84=3±142c^2-3c+1=0\Rightarrow c=\dfrac{3\pm\sqrt{9-8}}{4}=\dfrac{3\pm 1}{4}2c2−3c+1=0⇒c=43±9−8=43±1, so c=1c=1c=1 or c=12c=\dfrac12c=21. cosθ=1⇒θ=0∘, 360∘\cos\theta=1\Rightarrow \theta=0^\circ,\ 360^\circcosθ=1⇒θ=0∘, 360∘. cosθ=12⇒θ=60∘, 300∘\cos\theta=\dfrac12\Rightarrow \theta=60^\circ,\ 300^\circcosθ=21⇒θ=60∘, 300∘. θ=0∘, 60∘, 300∘, 360∘\boxed{\theta=0^\circ,\ 60^\circ,\ 300^\circ,\ 360^\circ}θ=0∘, 60∘, 300∘, 360∘