Solution Of Trigonometric Equations
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Find all the values of \(x\) between \(0\) and \(2 \pi\) for which
i) \(\cos x = \dfrac{1}{{\sqrt 2 }}\)
ii) \(\sin x = \dfrac{1}{2}\)
\begin{align}
&\begin{aligned}\text{i)}\quad \cos x=\frac{1}{\sqrt{2}} \\ x=\frac{\pi}{4}, \quad x &=2 \pi-\frac{\pi}{4} \\ x &=\frac{7 \pi}{4}
\end{aligned}\\
&\begin{aligned}\text{ii)}\quad \sin x=\frac{1}{2} \\ x=\frac{\pi}{6},\quad x &=\pi-\frac{\pi}{6} \\ &=\frac{5 \pi}{6}
\end{aligned}
\end{align}
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