mostly it comes from memorization. If sin 30 = 1/2, then arcsin (1/2) = 30
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Cosine(30) = sqrt(3)/2
It depends on what information you already have. For example, if you know the length of two sides of a triangle, you can easily find the tangent. Or, if you know the length of two angles and a side, you can find the other sides as well, using the tangent, cosine, and sine as needed.
usually its used to find a missing angle or length of a right triangle. Of course there is more to trigonometry. any way you can use sine, cosine, and tangent, to fine the missing angle or length
Use tangent to find the other leg, and the sine or cosine to find the hypotenuse.
you need to have at least 2 values of the lengths of the triangle and then you can find the angle by sine, cosine or tangent formulas you may try this online calculator for right triangles. http://www.rillocenter.com/calculate/trigonometry.html