Mathematics: Me with trigonometry. use trigonometric identities to solve 2cos^2(θ)=sin(θ)+1 exactly for 0≤θ 2π. if there is more than one answer, enter your answers as a comma separated list.

Me with trigonometry. use trigonometric identities

Ответ:

kaitie60

13.03.2022

$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\
-------------------------------\\\\
2cos^2(\theta )=sin(\theta )+1\implies 2[1-sin^2(\theta)]=sin(\theta )+1
\\\\\\
2-2sin^2(\theta )=sin(\theta )+1\implies 0=2sin^2(\theta )+sin(\theta )-1
\\\\\\\
0=[2sin(\theta )-1][sin(\theta )+1]\\\\
-------------------------------$

$\bf 0=2sin(\theta )-1\implies 1=2sin(\theta )\implies \cfrac{1}{2}=sin(\theta )\implies \measuredangle \theta =
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}
\end{cases}\\\\
-------------------------------\\\\
0=sin(\theta )+1\implies -1=sin(\theta )\implies \measuredangle \theta =\frac{3\pi }{2}$

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Ответ:

henrygrubb554

08.12.2020

Mathematics

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Me with trigonometry. use trigonometric identities to solve 2cos^2(θ)=sin(θ)+1 exactly for 0≤θ< 2π. if there is more than one answer, enter your answers as a comma separated list.

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