Trigonometry is a branch of mathematics that studies angles and the relationships between triangle sides and angles. It is widely used in fields such as physics, engineering, and architecture to solve problems involving angle and distance measurements.
Trigonometry is a branch of mathematics that studies angles and the relationships
between triangle sides and angles. It is widely used in fields such as physics,
engineering, and architecture to solve problems involving angle and distance
measurements.
The use of trigonometric functions, which are ratios of the sides of a right
triangle, is the foundation of trigonometry. The sine (sin), cosine (cos), and
tangent functions are the most commonly used trigonometric functions (tan). The
following functions are defined:
Sine (sin) = Contrary side / Hypotenuse
Adjacent side / Hypotenuse = cosine (cos).
Opposite side / Adjacent side = Tangent (tan).
In a right triangle, the hypotenuse is the longest side and is opposite the right
angle, while the adjacent side is adjacent to the angle of interest and the
opposite side is opposite the angle of interest.
Given the values of any two of these, the trigonometric functions can be used to
find the angles and sides of a right triangle. For example, if the lengths of the
adjacent side and hypotenuse are known, the cosine of the angle can be calculated
using the formula cos = adjacent side / hypotenuse.
Trigonometry can also be used to solve non-right triangles by combining the sine
and cosine laws. The law of sines states that the ratio of the length of one side
of a triangle to the sine of the angle opposite that side is the same for all sides
and angles of the triangle. The law of cosines describes the relationship between
triangle sides and angles, stating that the square of one side's length equals the
sum of the squares of the other two sides minus twice their product and the cosine
of the angle between them.
Trigonometry also covers many other topics, such as trigonometric identities,
inverse trigonometric functions, and the use of trigonometry in applications such
as navigation, astronomy, and music.
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