 Domain and Range of Sine and Cosine Functions - dummies

# Domain and Range of Sine and Cosine Functions

The sine and cosine functions are unique in the world of trig functions, because their ratios always have a value. No matter what angle you input, you get a resulting output. The value you get may be 0, but that’s a number, too. In reference to the coordinate plane, sine is y/r, and cosine is x/r.

The radius, r, is always some positive number (which is why these functions always have a value, because they don’t ask you to divide by 0), and r is always a number greater than (or equal to) the absolute value of x or y.

## Domains of sine and cosine

The domains of sine and cosine are infinite. In trig speak, you say something like this: If theta represents all the angles in the domain of the two functions which means that theta can be any angle in degrees or radians — any real number.

## Ranges of sine and cosine

The output values for sine and cosine are always between (and including) –1 and 1. In trig speak, it goes something like this: If represent the output values of the functions The ratios y/r and x/r will never be improper fractions — the numerator can never be greater than the denominator — because the value of r, the radius, is always the biggest number. At best, if the angle theta has a terminal side on an axis (meaning that one of the sides is equal to r), then the value of those ratios is 1 or –1.