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.
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.
Example 1:
Simplify the trigonometric expression [sin ^{6}x - cos ^{6}x] / [sin ^{4}x - cos ^{4}x].
Solution:
= [sin ^{2}x + cos ^{2}x] = 1
Example 2:
Simplify the trigonometric expression [sec(x) sin ^{4}x] / [[1 + sec(x)] Sin^{2}x].
Solution:
These are the trigonometry expression.