Trigonometry, as we all know, is the branch of mathematics that incorporates the concepts of ratios and angles of a right-angled triangle. Many students hate this topic due to its complexity and never-ending list of formulas and derivations. However, if the basics of this branch of Math are clear, then even the hardest problem will appear to be meek. The fundamental concept that must be learned by heart to excel in trigonometry is learning trigonometric ratios. The ratio of different sides of a triangle is known as trigonometric ratios. The trigonometric ratios can also be determined by either using the acute angles present inside the triangles or utilizing the length of the sides to formulate them. In general, there are six basic types of Trigonometric ratios, they are stated below:
For more details about the values of trigonometric standard angles, you can view a trigonometric table.
Let us learn about the trigonometric ratios one at a time:
Sine: The ‘Sine' is a trigonometric function that is abbreviated as Sin. Sine is the ratio of the size of the perpendicular of a right-angle triangle to its hypotenuse. Sin (k) = altitude (perpendicular) /hypotenuse or p/h, where ‘k’ is the angle present in between the two sides.
Cosine: The trigonometric function ‘Cosine' is shortened to ‘cos’ when used in trigonometric problems. Cosine is the ratio of the length of the base of a right-angle triangle to its hypotenuse. Cos (k) = base (bottom line) /hypotenuse or b/h, where ‘k’ is the angle present in between the two sides.
Tangent: Tangent is the trigonometric function defined as the ratio between the perpendicular of a right-angled triangle to its base. It is abbreviated as ‘tan’ and can be expressed as p/h. Interestingly, tan can also be defined as the ratio of the sin function of the triangle to the cos function of that triangle.
Tan (p) = sin (p) / cos (p).
These three complete the basics of trigonometric ratios. The other ratios are made by inverting these ratios. The multiplicative inverse is the process of implementing the reciprocal of a trigonometric ratio. They are also helpful and considered as the rudimentary ratios of trigonometry.
Cosecant: Cosecant, abbreviated as ‘cosec’ is the multiplicative inverse of the first trigonometric ratio, i.e., sine. Concerning a right-angle triangle, it can be referred to as the ratio of the hypotenuse to the perpendicular. Cosec (k) = 1/sin (k) or h/p.
Secant: The trigonometric ratio Secant is abbreviated as ‘sec’, and it is the multiplicative inverse of the second trigonometric ratio, i.e., cosine. It is defined as the ratio of the hypotenuse of a right-angle triangle to the base of the same triangle. Sec (k) = 1/cos (k) or h/b.
Cotangent: The last trigonometric ratio is Cotangent. It is abbreviated as ‘cot’ and is defined as the multiplicative inverse of the third trigonometric ratio, i.e., tan. A cot is expressed as the ratio of the base of a right-angle triangle to its perpendicular. We can also define it as the ratio of the cos function of a triangle to its sin function. Cot (k) = 1/tan (k), or b/p, or cos (k) / sin (k).