Year 11 Maths - Specialist Circular functions

Solution of equations involving sine and cosine

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Questions

Question 1

19207

Solve \(\cos \theta = -\dfrac{1}{2}\) for \({\theta ^o} \in [{\theta ^o},{360^o}]\)

Answer

\(\theta = {120^o},\theta = {240^o}\)

Worked Solution

\begin{align}
&\cos \theta=-\frac{1}{2}\\
&\begin{array}{cc}
\theta=180^{\circ}-60^{\circ}& \theta=180^{\circ}+60^{\circ} \\
=120^{\circ}\quad \;\;\,&=240^{\circ}\quad\;\;\;
\end{array}
\end{align}

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