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Beyond 360 degrees
The previous behavior repeats cyclically, so trigonometric functions are not limited to 360°. We can keep rotating counterclockwise, and once we reach 360 degrees, the sine and cosine functions start to repeat the same behavior. As a consequence, we can relate the functions at different angles with the following trig identities for any n integer: sin(θ + 2πn) = sin(θ); cos(θ + 2πn) = cos(θ); andFor example a trig function at 90° (π/2) will be mathematically the same as at 450° (5π/2), as 5π/2 = π/2 + 2π. Negative anglesNegative angles imply the same way to calculate sine and cosine (vertical and horizontal projections, respectively), with the difference that angular rotation occurs in the clockwise direction. For example, a trigonometric function at 270° is the same as at -90°, as their radial lines are the same (you can check it with this calculator) |
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