We can determine whether each of the other basic trigonometric functions is even, odd, or neither, with just these two facts and the reciprocal identities. Thus tangent takes the form f(−x)=−f(x), so tangent is an odd function. Therefore cotangent is also an odd function.

Is cotangent an odd function?

The tangent of an angle is the ratio of the y-value to the x-value of the corresponding point on the unit circle. The secant, cotangent, and cosecant are all reciprocals of other functions. ... Cosine and secant are even; sine, tangent, cosecant, and cotangent are odd.

How do you show that cotangent is an odd function?

Let cotx be the cotangent of x. Then, whenever cotx is defined: cot(−x)=−cotx. That is, the cotangent function is odd.