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Comparison of graphs of the parabolas x(180 − x)/8100 and x(180 − x)/9000 with the graph of sin x (with x in degrees) The part of the graph of sin x in the range from 0° to 180° "looks like" part of a parabola through the points (0, 0) and (180, 0). The general form of such a parabola is (). The parabola that also passes through (90, 1 ...
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1]
The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
Using this standard notation, the argument x for the trigonometric functions satisfies the relationship x = (180x/ π)°, so that, for example, sin π = sin 180° when we take x = π. In this way, the degree symbol can be regarded as a mathematical constant such that 1° = π /180 ≈ 0.0175.
The fixed point iteration x n+1 = cos(x n) with initial value x 0 = −1 converges to the Dottie number. Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is sin ( 0 ) = 0 {\displaystyle \sin(0)=0} .
Fig. 1 Isosceles skinny triangle In trigonometry , a skinny triangle is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians .