Ad
related to: subtended by chord at a point value of 2 0 and 5 x 7 notepadsuprinting.com has been visited by 10K+ users in the past month
Search results
Results From The WOW.Com Content Network
More generally, an angle subtended by an arc of a curve is the angle subtended by the corresponding chord of the arc. For example, a circular arc subtends the central angle formed by the two radii through the arc endpoints. If an angle is subtended by a straight or curved segment, the segment is said to subtend the angle.
The angle θ is taken in the positive sense and must lie in the interval 0 < θ ≤ π (radian measure). The chord function can be related to the modern sine function, by taking one of the points to be (1,0), and the other point to be (cos θ, sin θ), and then using the Pythagorean theorem to calculate the chord length: [2]
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
The word jīvá is also used as a synonym for jyā in geometrical literature. [2] At some point, Indian astronomers and mathematicians realised that computations would be more convenient if one used the halves of the chords instead of the full chords and associated the half-chords with the halves of the arcs.
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
The formulas for addition and subtraction involving a small angle may be used for interpolating between trigonometric table values: Example: sin(0.755) = (+) + () + () where the values for sin(0.75) and cos(0.75) are obtained from trigonometric table. The result is accurate to the four digits given.
For example, where the length of a chord subtended by a 112° arc is reported to be 99,29,5, it has a length of + + = ¯, rounded to the nearest 1 / 60 2 . [1] After the columns for the arc and the chord, a third column is labeled "sixtieths". For an arc of θ°, the entry in the "sixtieths" column is
(For a non-unit sphere, the lengths are the subtended angles times the radius, and the formula still holds if a, b and c are reinterpreted as the subtended angles). As a special case, for C = π / 2 , then cos C = 0, and one obtains the spherical analogue of the Pythagorean theorem: =