How do you find the interval of decrease and increase of a sin function? Given this function f(x) = sin2x-90degrees What is the interval of...

f(x)=sin2x -90

The function
f(x) is incresing when f'(x) is >0.

f'(x) = (sin2x
-90)' = 2cos2x

2co2x > 0 implies cos2x >
0

Cos2x > 0 when  2npi-pi/2 < 2x <
2npi-pi.

Cos2x > 0 when  -pi/4 < x
<pi/4. That is when x is in (npi/2-pi/4 , npi/2+pi/4),  n =
0,1,2,..

Therefore sin2x - 90 is increasing in (npi-pi/4
,npi+ pi/4).

 Or

When x  is  
in the interval (180n-45 deg ,180n+45 deg ) for n
=0,1,2,....

Sin2x -90 is decreasing  when (sin2x-90)'
< 0. Or

2cos2x < 0 or cos2x <
0.

cos2x < 0 when 2npi+ pi/2 < 2x <
2npi+3pi/2.

Or

npi+Pi/4
< x < npi+3pi/4 is  same as when x is in (180n+45deg to 135 deg.), n
=0,1,2,3....

Therefore sin2x-90 is decreasing in (180n+45
deg , 180n+135deg), for n = 0,1,2,3....