Final answer:
The cosine function and the sine function are related by the identity cos(x°) = sin(90 - x°) due to the periodic nature of the sine function with a period of 360 degrees, an infinite number of x values can prove this identity true.
Step-by-step explanation:
In trigonometry, the cosine function and the sine function are related by the identity cos(x°) = sin(90 - x°).
This means that for any angle x, the cosine of x degrees is equal to the sine of the complementary angle (90 - x) degrees.
The reason there are an infinite number of x values that prove this identity true is because the sine function is periodic, meaning it repeats itself at regular intervals.
Since the sine function has a period of 360 degrees, any angle and its corresponding complementary angle (90 - x) degrees will have the same sine values.
For example, if x = 30 degrees, then 90 - x = 60 degrees.
The sine of 30 degrees is the same as the sine of 60 degrees, which is 0.5.