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[Solved] Domain and range of the trigonometric function

 
Trigonometry 1 & 2
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June 15, 2021 3:01 pm
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(@armor)
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June 15, 2021 3:02 pm
Topic starter
Staff 
(@armor)
Admin
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317 Posts
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The function is defined if and only if   \small 2cosx-1\geq 0,  that is   \small cosx\geq \frac{1}{2}.  Thus the domain of y is   \small 2n\Pi -\frac{\Pi }{3}\leq x\leq 2n\Pi +\frac{\Pi }{3} (n\epsilon \mathbb{Z}).

Since \small 0\leq \sqrt{2cosx-1}\leq 1,  then  \small 0\leq arctan\sqrt{2cosx-1}\leq \frac{\Pi }{4},   thus  \small \frac{\Pi }{8}\leq y\leq \frac{\Pi }{4}.

Therefore, the domain of the function is \small x\epsilon [2n\Pi -\frac{\Pi }{3},2n\Pi +\frac{\Pi }{3}] (n\epsilon \mathbb{Z}),   and the range is  \small y\epsilon [\frac{\Pi }{8},\frac{\Pi }{4}].

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