Which trigonometric functions can take the value $0$ ?

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Answer 1 · 2016-05-08T12:52:44

Of the six basic trigonometric functions, the ones which take the value $0$ for some value of the argument are:

$sin, cos, tan, cot$

The other two do not:

$sec, csc$

$sin theta = 0$ and $tan theta = 0$ when $theta = k pi$ for some integer $k$

$cos theta = 0$ and $cot theta = 0$ when $theta = pi/2 + k pi$ for some integer $k$

For any Real angle $theta$ , we have:

$abs(sec theta) >= 1$

$abs(csc theta) >= 1$

so these functions are never zero.

Which trigonometric functions can take the value 00 ?