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9.6 trigonometric equations

ALNote, the magic 5 steps
[alpha, equal, shift trigo, take positive, decide quadrants]

Example:
Solve each of the following trigonometric equations for 0^\circ ≤ x ≤ 360^\circ
a) \sin\theta = -\frac{1}{\sqrt 2}

b) \tan \theta = \sqrt 3

c) \cos 2\theta = - \frac{\sqrt 3}{2}

Solution:
a
\sin\theta = -\frac{1}{\sqrt 2}
\alpha=\sin^{-1}(\frac{1}{\sqrt 2}),\;Q_3,\;Q_4
\alpha=45^\circ

\theta=Q_3,\;Q4
\theta=180^\circ + \alpha, \; 360^\circ - \alpha
\theta=225^\circ,\;315^\circ

b
\tan\theta=\sqrt 3

Learning Mathematics