What are the units of sine and cosine? do they depend on the units of the angle (degrees or radians)?

Question

What are the units of sine and cosine? do they depend on the units of the angle (degrees or radians)?

Answer 1

Sine and cosine are functions and have no units. The ratios returned by the sine and cosine functions are also unitless. Angles can be in degrees or radians, but these are dimensionless units, meaning they don't represent a physical quantity, such as mass or length.

Answer 2

Trigonometric functions are ratios, and hence, are dimensionless.

You can "calculate" with units of measure in a fashion similar to numbers.  Suppose you measure the sides of the triangle in feet and get the following results:

y = 2 ft

r = 5 ft

Then, sin(T) = 2 ft / 5 ft

When you divide a number by itself, it "cancels out" and becomes one.  The same happens with the units.  The feet "cancel out" and leave no units for the resulting ratio.

Hence, sin(T) = 0.40