Final answer:
The question seeks sine and cosine functions with specific phase shifts, derived from the definitions of the ratios in trigonometry and the periodic nature of these functions, which oscillate between -1 and 1 and repeat every 2π radians.
Step-by-step explanation:
The question involves determining sine and cosine functions based on given criteria, which are essentially phase-shifted versions of the standard sine and cosine functions. These functions relate to the trigonometric ratios derived from a right-angled triangle, where the sine of an angle is the ratio of the length of the opposite side to the hypotenuse, and the cosine is the ratio of the adjacent side to the hypotenuse. By taking into account the periodic nature of these trigonometric functions, where sine and cosine repeat every 2π radians and their values oscillate between -1 and 1, we can determine the requested functions.
Example Functions
- y = sin(x + 60°) is a sine function with a phase shift to the left by 60 degrees.
- y = cos(x - 60°) is a cosine function with a phase shift to the right by 60 degrees.
In each case, the phase shifts are applied according to the co-terminal angle properties, which can be utilized to simplify the expressions through periodicity. This means the functions will have the same values at co-terminal angles, where angles are separated by full revolutions of 360° or 2π radians.