Additional Mathematics Topical 2011 to 2015
Category Archives: Additional Mathematics 0606
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