Answer:
A function is strictly increasing in the interval where the derivate is positive.
Then we must look at the derivate of sin(x)
if f(x) = sin(x)
f'(x) = cos(x)
Then we must see which vales make cos(x) positive.
cos(0) = 1.
cos(90°) = 0
cos(-90°) = 0.
Then the cos(x) function is positive in the range (-90°, 90°) (notice that it is an open interval).
Then the function sin(x) will be strictly increasing in the interval (-90°, 90°)
And because these functions are periodic, where the period is 360°, we can actually write this interval as:
(-90° + n*360°, 90° + n*360°) where n is an integer number.
