Trigonometry is a branch of mathematics that deals with the relationships between sides and angles of triangles.
Trigonometric functions are used to determine the relationship between the lengths of the sides of a right-angled triangle based on the interior angles of the triangle.
The simplest way to explain the definition of trigonometric functions in a right-angled triangle.
How?
In a right-angled triangle, there is an acute angle opposite a right angle which we denote by the Greek letter alpha. The sides of the triangle ‘a’ and ‘b’ are called perpendiculars because they are at the right angle, and side ‘c’ is called the hypotenuse. Given the above, we can proceed to the derivation of the trigonometric functions.
In a triangle we find four basic functions:
- sinus - sin - sin of the angle alpha = a/c - it is the ratio of the length of the side that is opposite that angle (a) to the length of the hypotenuse (c)
- cosine - cos - cos of the angle alpha = b/c - the ratio of the length of the side adjacent to the angle (b) to the length of the hypotenuse (c).
- tangent - tg - tg of the angle alpha = a/b - it is the ratio of the length of sidethat is opposite the angle (a) to the length of the side adjacent to the angle (b)
- cotangents - ctg - ctg of the angle alpha = b/a - it is the ratio of the length of side b (adjacent) to the length of side a (opposite)
Some formulas of trigonometric functions
- formula for trigonometric singularity
sin2α+cos2α=1
- formula for tangents
tgα=sinα/cosα
- formula for cotangents
ctgα=cosα/sinα
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