Trigonometry Expression

Introduction  

           Trigonometry deals with the angle and side of triangles. Unknown angles or lengths are evaluated by using trigonometrical ratios such as sine, cosine, and tangent. Trigonometry used in the fields of navigation, astronomy and surveying, and usually involved working out an inaccessible distance.Trigonometry used to find the distance of the Earth from the Moon. Trigonometric ratios of acute angles as the ratio of the sides of a right angled triangle.

 

Trigonometric functions on trigonometry expression:

 

        Some trigonometry functions are given below:

                  SIN = OPPOSITE / HYPOTENUSE

                  COS = ADJACENT / HYPOTENUSE

                  TAN = OPPOSITE / ADJACENT

                  COT = ADJACENT / OPPOSITE

                  SEC = HYPOTENUSE / ADJACENT

                  COSEC = HYPOTENSE / OPPOSITE

        The right angle sided of the triangle consists of any value of all sides and the lengths will be the same for all right triangles either the triangle may be Large or small; the ratio present only depend on the angles and not on the length which is actual the functions which in pair that is sine and cosine, tangent and cotangent, secant and co-secant called co functions.

 

Examples for Trigonometry Expression:

 

Example 1:

 Simplify the trigonometric expression [sin 6x - cos 6x] / [sin 4x - cos 4x].

Solution:

  • Factor the denominator

    [sin 6x - cos 6x] / [sin 4x - cos 4x]

    = [sin 2x - cos 2x] [sin 2x + cos 2x] [sin 2x - cos 2x] / [sin 2x - cos 2x]  [sin 2x - cos 2x] and simplify

      = [sin 2x + cos 2x] = 1

 

Example 2:

 Simplify the trigonometric expression [sec(x) sin 4x] / [[1 + sec(x)] Sin2x].

Solution:

  • Substitute sec (x) is in the numerator by 1 / cos (x) and simplify.

    [sec(x) sin 4x] / [[1 + sec(x)] Sin2x]

    = sin 4x / [ [cos x (1 + sec (x) ] Sin2x]

    = sin 2x / [ cos x + 1 ]

 These are the trigonometry expression.