You can calculate that on any scientific calculator. Just make sure that the calculator is set to "degrees". As a check, the sine of 90° should come out as exactly 1.
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sin(30) = 1/2
The sine of 1 (rad) is 0.8414709848078965066525023216303.The sine of an angle of 1 degree (from the computer's calculator) is 0.017452406 (correct to 9 decimal places).
Yes, the sine, cosine and tangent are integral to problem solving (angles and side lengths) in right angle triangles (triangles with a 90 degree angle included).
The number 1.414... (square root of 2) is two times the cosine or sine of a 45 degree angle. The reason for this is that for a 45 degree angle, the two sides are cosine and sine, they are equal, and if you solve using the Pythagorean theorem with a hypotenuse of 1, the two sides are each (21/2)/2.
the sine of an angle can't be greater than 1.0