opticaltempest
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I have a question when solving trigonometric equations.
For example:
Find all the solutions in the interval [0,2pi)
\sin \theta \tan \theta = \sin \theta \]
If you choose to divide through by \sin \theta\] we get,
\tan \theta = 1\] such that \sin \theta \ne 0\]
otherwise we are essentially dividing both sides by zero, which we
cannot do.
Do we need to be careful when solving trigonometric equations using
multiplication and division?
We're dividing by a term that can take on the value of zero. Does
this have any special name? How can I learn more about this?
Are there any techniques to use when solving trig equations
so this doesn't happen?
For example:
Find all the solutions in the interval [0,2pi)
\sin \theta \tan \theta = \sin \theta \]
If you choose to divide through by \sin \theta\] we get,
\tan \theta = 1\] such that \sin \theta \ne 0\]
otherwise we are essentially dividing both sides by zero, which we
cannot do.
Do we need to be careful when solving trigonometric equations using
multiplication and division?
We're dividing by a term that can take on the value of zero. Does
this have any special name? How can I learn more about this?
Are there any techniques to use when solving trig equations
so this doesn't happen?