Which trigonometric functions can take the value #0# ?

1 Answer
May 8, 2016

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#

Explanation:

#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.