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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] In the table below, the label "Undefined" represents a ratio :
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
ISO 5775 is an international standard for labeling the size of bicycle tires and ... 26 × 1 + 3 ⁄ 8 × 1 + 1 ... (see the standard for drawings and exact ...
For example, if a fat-bike tire is inflated to 0.5 bar (50 kPa; 7.3 psi) gauge pressure at room temperature 20 °C (68 °F) and then the temperature is decreased to −10 °C (14 °F) (a 9% decrease in absolute temperature), the absolute pressure of 1.5 bar (150 kPa; 22 psi) will be decreased by 9% to 1.35 bar (135 kPa; 19.6 psi), which ...
The values for a/b·2π can be found by applying de Moivre's identity for n = a to a b th root of unity, which is also a root of the polynomial x b - 1 in the complex plane. For example, the cosine and sine of 2π ⋅ 5/37 are the real and imaginary parts , respectively, of the 5th power of the 37th root of unity cos(2π/37) + sin(2π/37)i ...
Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.
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.
Bicycle tires usually have a marking on the sidewall indicating the pressure appropriate for that tire. Bicycles use much higher pressures than cars: car tires are normally in the range of 30 to 40 pounds per square inch (210 to 280 kPa), whereas bicycle tires are normally in the range of 60 to 100 pounds per square inch (410 to 690 kPa).
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