The distance from a point to the origin is always positive, but the signs of the x and y coordinates may be positive or negative. Thus, in the first quadrant, where x and y coordinates are all positive, all six trigonometric functions have positive values. In the second quadrant, only sine and cosecant (the reciprocal of sine) are positive. In the third quadrant, only tangent and cotangent are positive. Finally, in the fourth quadrant, only cosine and secant are positive. The following diagram may help clarify.

When an angle lies along an axis, the values of the trigonometric functions are either 0, 1, -1, or undefined. When the value of a trigonometric function is undefined, it means that the ratio for that given function involved division by zero. Below is a table with the values of the functions for quadrantal angles.

The points at which the values of a function are undefined are technically not in the domain of that function. Therefore, the domain of sine and cosine is all real numbers. The domain of tangent and secant is all real numbers except + kπ, where k is an integer. The domain of cosecant and cotangent is all real numbers except kπ, where k is an integer.