Question

How do you evaluate the sine, cosine, and tangent of the angle 30 degrees without using a calculator?

Answer 1

Sine: `1/2`
Cosine: `sqrt3/2`
Tangent: `sqrt3/3`

Explanation:

Well in my country, you simply must know, since you won't keep doing the trigonometric relations on a circle over and over again to understand them. There are some quick ways to get it on your head:

You only need to know the values that belong in 30, 45 and 60 degrees. Since the other ones can be found by simple metric relations:

180-x, 180+x, 360-x and they will have the same values since they are simetric to 30, 45 and 60.

For example 180-30 = 150. The sin of 30 and 150 is `1/2` or 180-60 = 120. The sin of 60 and 120 is `sqrt3/2`