Year 11 Maths - Specialist Circular functions

General solution of trigonometric equations

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Questions

Question 1

20987

Find the general solution of \(\tan \left( {\theta - \dfrac{\pi }{3}} \right) = - \sqrt 3 \)

Answer

\(\theta = n\pi \)

Worked Solution

\begin{align*}
\tan \left(\theta-\frac{\pi}{3}\right) &=-\sqrt{3} \\
\therefore \theta-\frac{\pi}{3} &=n \pi+\tan ^{-1}(-\sqrt{3}) \\
\theta-\frac{\pi}{3} &=n \pi-\frac{\pi}{3} \rightarrow \theta=n \pi
\end{align*}

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