Overview of Trigonometric Function

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 Trigonometric functions are mathematical functions that relate to the angles and sides of a right-angled triangle. These functions are widely used in mathematics, science, and engineering to solve problems related to angles, distances, and waves.

The three primary trigonometric functions are sine, cosine, and tangent, which are commonly denoted as sin(x), cos(x), and tan(x), respectively. These functions are defined as follows:

  • Sine: sin(x) = opposite/hypotenuse
  • Cosine: cos(x) = adjacent/hypotenuse
  • Tangent: tan(x) = opposite/adjacent

Here, x is the angle in degrees or radians, opposite and adjacent are the lengths of the sides of the right-angled triangle, and hypotenuse is the longest side of the triangle.

Other trigonometric functions include cosecant, secant, and cotangent, which are defined as the reciprocals of sine, cosine, and tangent, respectively.

Trigonometric functions have many applications, including in navigation, physics, engineering, and architecture. They are used to solve problems related to distance, velocity, acceleration, and oscillation, among others.

In addition to their practical applications, trigonometric functions have also been studied extensively in mathematics, where they are used to study the properties of functions, solve equations, and prove theorems.

here is a table of trigonometric ratios for common angles in degrees:

Angle (degrees)Sin (opposite/hypotenuse)Cos (adjacent/hypotenuse)Tan (opposite/adjacent)Cosec (hypotenuse/opposite)Sec (hypotenuse/adjacent)Cot (adjacent/opposite)
0°010undefined1undefined
30°1/2√3/2√3/322/√3√3
45°√2/2√2/21√2√21/√2
60°√3/21/2√32/√321/√3
90°10undefined1undefined0

Note that for angles of 0° and 90°, the tangent and cotangent are undefined, and for angles of 30°, 60°, and 90°, the cosecant and secant are irrational numbers.

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