Find every angle theta with 0≤θ≤2π radians, and 2sin2(θ)+cos⁡(θ)=2

sin2=1−cos2, so using x as θ,2−2cos2x+cos⁡x=2, 2cos2x−cos⁡x=0,cos⁡x(2cos⁡x−1)=0, cos⁡x=0or0.5 x=π3or60°,π2or90°,3π2or270°,5π3or300°.

"Find every angle theta with 0≤θ≤2π radians, and" was answered by our community

sodni3

2021-02-25

Find every angle theta with $0 \leq θ \leq 2 π r a d i a n s, a n d 2 \sin^{2} (θ) + \cos (θ) = 2$

Margot Mill

Skilled2021-02-26Added 106 answers

\sin^{2} = 1 - \cos^{2},

so using x as

θ, 2 - 2 \cos^{2} x + \cos x = 2,

2 \cos^{2} x - \cos x = 0, \cos x (2 \cos x - 1) = 0,

\cos x = 0 or 0.5

x = \frac{π}{3} or 60 °, \frac{π}{2} or 90 °, 3 \frac{π}{2} or 270 °, 5 \frac{π}{3} or 300 ° .

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