How to Understand Trigonometric Functions

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Trigonometry is the field of mathematics involving the measure of triangles. It is useful in the fields of astronomy, physics, surveying, engineering, navigation and other scientific fields. A triangle consists of three sides and in reference to an angle each side is named adjacent, opposite, and hypotenuse. Except for an equilateral triangle where all sides are equal, the hypotenuse is the side with the longest length. The opposite side is the side opposite of the reference angle and the remaining side is called adjacent. The six major trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.

  • The sine of an angle is the ratio of the opposite side divided by the adjacent side. The sine of angle A is indicated by ‘sin A’.
  • Cosine is the ratio of the adjacent side divided by the hypotenuse. The cosine of angle A is indicated by ‘cos A’.
  • Tangent is the ratio of the opposite side divided by the adjacent side. The tangent of angle A is indicated by ‘tan A’.
  • Cotangent is the ratio of the adjacent side divided by the opposite side. The cotangent of angle A is indicated by ‘cot A’.
  • Secant is the ratio of the hypotenuse divided by the adjacent side. The secant of angle A is indicated by ‘sec A’.
  • Cosecant is the ratio of hypotenuse divided by the opposite side. The cosecant of angle A is indicated by ‘csc A’.

Note that there are relationships between the functions: sin A = 1/csc A, cos A= 1/sec A, tan A=1/cot A, csc A=1/sin A, sec A=1/cos A, and cot A=1/tan A.

Other relationships include tan A = sin A/cos A and sin2 A + cos2 A = 1

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