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The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. 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.
However, when it is inconvenient to use base-60 for minutes and seconds, positions are frequently expressed as decimal fractional degrees to an equal amount of precision. Degrees given to three decimal places ( 1 / 1000 of a degree) have about 1 / 4 the precision of degrees-minutes-seconds ( 1 / 3600 of a degree) and ...
A geographical mile is defined to be the length of one minute of arc along the equator (one equatorial minute of longitude) therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1 ...
A nautical mile is a unit of length used in air, marine, and space navigation, and for the definition of territorial waters. [2] [3] [4] Historically, it was defined as the meridian arc length corresponding to one minute ( 1 / 60 of a degree) of latitude at the equator, so that Earth's polar circumference is very near to 21,600 nautical miles (that is 60 minutes × 360 degrees).
The cosine of the hour angle (cos(h)) is used to calculate the solar zenith angle. At solar noon, h = 0.000 so cos(h) = 1, and before and after solar noon the cos(± h) term = the same value for morning (negative hour angle) or afternoon (positive hour angle), so that the Sun is at the same altitude in the sky at 11:00AM and 1:00PM solar time. [5]
Approximately equal behavior of some (trigonometric) functions for x → 0. For small angles, the trigonometric functions sine, cosine, and tangent can be calculated with reasonable accuracy by the following simple approximations:
It is denoted by a double prime ( ″ ). For example, 3° 7′ 30″ is equal to 3 + 7 / 60 + 30 / 3600 degrees, or 3.125 degrees. The arcsecond is the angle used to measure a parsec: grad: 400: 0°54′ The grad, also called grade, gradian, or gon. It is a decimal subunit of the quadrant. A right angle is 100 grads.
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...