Final answer:
The domain for both sine and cosine functions is all real numbers, and the range is from -1 to 1.
Step-by-step explanation:
The domain of both the sine and cosine functions is all real numbers, as they are defined for any angle measured in radians. This means for any value 'x', there exists a value for sin(x) and cos(x).
The range for both the sine and cosine functions is from -1 to 1. No matter the value of 'x', sin(x) and cos(x) will not exceed these bounds since they represent the ratio of sides in a unit circle and can never be greater than the radius of the circle, which is 1.
Now, comparing the sine and cosine functions, they are similar in their domains and ranges. However, their values differ based on the angle.
Initial conditions are different for the sine and cosine functions. For a sine function with zero phase shift, the initial position is 0, the initial velocity is maximum, and the initial acceleration is 0.
For a cosine function with zero phase shift, the initial position is maximum, the initial velocity is 0, and the initial acceleration is at its maximum (in the negative direction).
S, these functions share the same domain and range, sine and cosine differ in their values at a given angle, which affects the initial conditions in harmonic motion and circular motion scenarios.