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

1 Answer
Bruno09
Jun 28, 2015

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:

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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#

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