Which trigonometric functions can take the value #0# ?

Question

2557 views around the world

You can reuse this answer
Creative Commons License

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.