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For tiny arcs, the chord is to the arc angle in degrees as π is to 3, or more precisely, the ratio can be made as close as desired to π / 3 ≈ 1.047 197 55 by making θ small enough. Thus, for the arc of 1 / 2 °, the chord length is slightly more than the arc angle in degrees. As the arc increases, the ratio of the chord to ...
The half-angle formula for sine can be obtained by replacing with / and taking the square-root of both sides: (/) = () /. Note that this figure also illustrates, in the vertical line segment E B ¯ {\displaystyle {\overline {EB}}} , that sin 2 θ = 2 sin θ cos
In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained. By symmetry, the bisected side is half of the side of the equilateral triangle, so one concludes = /.
The 1 in 60 rule used in air navigation has its basis in the small-angle approximation, plus the fact that one radian is approximately 60 degrees. Interpolation [ edit ]
It is unknown whether these constants are transcendental in general, but Γ( 1 / 3 ) and Γ( 1 / 4 ) were shown to be transcendental by G. V. Chudnovsky. Γ( 1 / 4 ) / 4 √ π has also long been known to be transcendental, and Yuri Nesterenko proved in 1996 that Γ( 1 / 4 ), π, and e π are algebraically independent.
1.55 g [b] Gravitron amusement ride 2.5–3 g: Gravity of Jupiter at its mid-latitudes and where atmospheric pressure is about Earth's 2.528 g: Uninhibited sneeze after sniffing ground pepper [27] 2.9 g: Space Shuttle, maximum during launch and reentry 3 g: High-g roller coasters [10]: 340 3.5–12 g: Hearty greeting slap on upper back [27] 4.1 g
[18] [19] Today, the degree, 1 / 360 of a turn, or the mathematically more convenient radian, 1 / 2 π of a turn (used in the SI system of units) is generally used instead. In the 1970s – 1990s, most scientific calculators offered the gon (gradian), as well as radians and degrees, for their trigonometric functions . [ 23 ]
Rankine (°R or °Ra), which uses the Fahrenheit scale, adjusted so that 0 degrees Rankine is equal to absolute zero. Unlike the degree Fahrenheit and degree Celsius, the kelvin is no longer referred to or written as a degree (but was before 1967 [1] [2] [3]). The kelvin is the primary unit of temperature measurement in the physical sciences ...