To find where the sin(x) function is greater than the cos(x) function, we must first define the interval of values for x where we need to compare the two functions.
In mathematics, the functions of sine and cosine are cyclical and repeat their values every 2π radians or every 360 degrees. They both range from -1 to 1, and they are equal to each other at two points in one cycle: 45 and 225 degrees or π/4 and 5π/4 radians respectively. So, let's take a closer look at the interval from 0 to 90 degrees or 0 to π/2 radians(since we're interested in x values where sin(x) > cos(x), we can think about the first quarter of their cycle).
At 0 (0 degrees or 0 radians), sin(x) is 0 and cos(x) is 1.
At π/2 or 90 degrees, cos(x) is 0, and sin(x) is 1.
So, for values between 0 and π/2 radians (or 0 to 90 degrees), the sin(x) function starts at 0 and increases to 1, while the cos(x) function starts at 1 and decreases to 0.
So the sine function is greater than the cosine function in the interval (0, π/2) in radians or (0, 90) in degrees. So, we have the two ranges:
In radians: (0, π/2) or approximately (0, 1.57).
In degrees: (0, 90).
And that's the result, the x-values where sin(x) is greater than cos(x) lie between 0 and π/2 radians, or between 0 and 90 degrees.