# How to turn sin, cos, and tan into radicals.For example, how to turn tan30 into a radical.

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sciencesolve | Certified Educator

You need to know that sin, cos and tan are trigonometric functions and some of the values of these functions are expressed using irrational numbers.

Take several values between 0 and 90 degrees.

Take the angle of 30 degrees:

`sin 30 = 1/2 ; cos 30 = sqrt3/2 and tan 30 = sin 30/ cos 30 = sqrt3/3`

Take the angle of 45 degrees:

`sin45 = sqrt 2/2 ; cos45 = sqrt2/2 and tan45 = sin 45/ cos45 = 1`

Take the angle of 60 degrees:

`sin 60 = sqrt3/2 ; cos 60 = 1/2 and tan 30 = sin 60/ cos 60 = sqrt3`

**Therefore, in some of the values of the functions sine, cosine and tangent you may find irrational numbers (radicals).**