Resolved: "Solve sin⁡(2x)−cos⁡(x)=0 over the interval 0 to 2π."

Sandra Allison

Answered question

2021-12-09

Solve

\sin (2 x) - \cos (x) = 0

over the interval

0

2 π

Foreckije

Beginner2021-12-10Added 32 answers

Use the identity

\sin (2 x) = 2 \sin (x) \cos (x)

2 \sin (x) \cos (x) - \cos (x) = 0

\cos (x) (2 \sin (x) - 1) = 0

Set both of these terms equal to 0

\cos (x) = 0 \Rightarrow x = \frac{π}{2}, \frac{3 π}{2}

2 \sin (x) - 1 = 0 \Rightarrow \sin (x) = \frac{1}{2} \Rightarrow x = \frac{π}{6}, \frac{5 π}{6}

Corgnatiui

Beginner2021-12-11Added 35 answers

Thanks.

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