Why Is Cotangent an Odd Function?

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.