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A circle with an equilateral chord (red). One sixtieth of this arc is a degree. Six such chords complete the circle. [6] The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.
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.
Convert all angles to corresponding points on the unit circle, e.g., ... Consider the following three angles as an example: 10, 20, and 30 degrees. Intuitively ...
[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]
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, and west 270°. ... abbreviated "S30°E", which is the bearing 30 degrees in the eastward ...
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Special angle-based triangles inscribed in a unit circle are handy for visualizing and remembering trigonometric functions of multiples of 30 and 45 degrees. Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed.