Question #6f857

1 Answer
Max G.
Jul 19, 2017

Go with the angles that you know!

Explanation:

#sintheta = 0#
Whenever #theta# is an integer multiple of #pi#.
We write #theta = npi#.

In this case
#sin(sinx) = 0#
if and only if
#sinx = npi#
where n is an integer.
Since #sinx# may not equal #pi#, #2pi#, or any other value outside of the interval [-1, 1],
#sinx = npi#
if and only if
#sinx = 0#
This occurs when x is a multiple of #pi#.

So...
if #x = mpi#, where m is an integer,
then #sin(sinx) = sin(0) = 0#.

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