Question

Which trigonometric functions do not have real zeros?

sine, cosine, tangent, cosecant, secant, or cotangent.

Answer 1

secant and cosecant have no zeroes.

Explanation:

We have in total 6 trignometric functions as

sine, cosine, tangent, cosecant, secant, or cotangent.

Of these we have

sin is 0 for all multiples of pi

cosec = 1/sin cannot be zero since sine value is always finite lies between -1 and 1.

Similarly sec = 1/cos cannot be zero since cosine value is always finite lies between -1 and 1.

cotangent can be 0 for odd multiples of pi/2

Hence answer is only

secant and cosecant

Answer 2

cosecant, secant, and cotangent do not have real zeros.