Chapter 5

Trigonometry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Trigonometry is a branch of mathematics with a wide range of practical applications. Its concept was given by the Greek mathematician Hipparchus. You must have learnt basic trigonometry during your maths classes and surely must be wondering what is trigonometry and trigonometric ratios of complementary angles? Trigonometry finds its use not only in maths but also in other subjects, including science and engineering. You can even use trigonometry in solving your numerous geometrical problems without using the base geometrical concepts. This article explores the basic concept of trigonometry, which is useful for your coming exams and other competitive examinations.

Basic trigonometry deals with three fundamental ratios, namely the sine, cosine and tan ratios. These ratios correspond to the ratios of the different sides of a right-angled triangle. The whole trigonometry ratios are based on the right triangle. The basic trigonometric functions for the right-angled triangle are given below.

In the above triangle, angle B is a right angle. Hence, now we can calculate different trigonometric ratios for the above triangle.

  • Sine: Sine is the ratio of the opposite side to the hypotenuse.
  • Cosine: Cosine is the ratio of the adjacent side to the hypotenuse.
  • Tangent: Tan function is the ratio of the opposite side to the adjacent side.
  • Cosecant: Cosec is the ratio of the hypotenuse to the opposite side.
  • Secant: Sec is the ratio of the hypotenuse to the adjacent side.
  • Cotangent: Cotan is the ratio of the adjacent side to the opposite side.
RatioSide
Sine ABC/AC
Cosine AAB/AC
Tangent ABC/AB
Cotangent AAB/BC
Cosec AAC/BC
Sec AAC/AB

Some of the applications of trigonometry are given below.

  • In real-world geometry, trigonometric ratios are used to find the heights and distances from a particular point. For example, if you are seeing a huge skyscraper in front of you and want to figure out the skyscraper’s height, simply using the elevation angle and the horizontal distance between you two is enough to find the height of the skyscraper.
  • Trigonometry is extensively used in engineering and drawing subjects for building models and prototypes.
  • It is used in physics for determining various physical parameters of any machine/object.

While solving various algebraic expressions, you can easily use trigonometric identities to get to the answer quickly. As we said before, you can use trigonometric ratios for solving even traditional geometrical problems. Sine, cosine, and tangent are the three basic trigonometric identities. The rest of the identities are based on these. Hence, explore these three basic identities, and you can follow up with the rest.

Trigonometric ratios of complementary angles include the identity of two angles whose sum is 90 degrees. Therefore, if we have an angle A, then its complementary angle will be 90-A.

Trigonometry is considered an ancient mathematical tool developed during the Greek period of Hipparchus. We know that there are many great Greek mathematicians and philosophers that gave us some of the best mathematical concepts that still find their use. There are six main trigonometric functions that are used throughout the trigonometric concepts. These trigonometric functions are used in various applications such as navigation, mapping, engineering and more.

  1. What are trigonometric ratios?
    Trigonometric ratios are the ratios of sides in the right-angled triangle corresponding to a definite angle. Hence from a given reference angle, we can have six unique trigonometric ratios associated with it that can be used to find the heights and distances, including the solution to your questions.
  2. What are the three primary trigonometric ratios?
    The three basic trigonometric ratios are the sine, cosine and tangent ratios that correspond to the ratio of the different sides of the right-angled triangle. The meaning of the different trigonometric ratios is given below.
    Sine: Sine is the ratio of the opposite side to the hypotenuse.
    Cosine: Cosine is the ratio of the adjacent side to the hypotenuse.
    Tangent: Tan function is the ratio of the opposite side to the adjacent side.
  3. What are the six different trigonometric function formulas?
    The six different trigonometric function values are given as follows.
    Sine: Sine is the ratio of the opposite side to the hypotenuse.
    Cosine: Cosine is the ratio of the adjacent side to the hypotenuse.
    Tangent: Tan function is the ratio of the opposite side to the adjacent side.
    Cosecant: Cosec is the ratio of the hypotenuse to the opposite side.
    Secant: Sec is the ratio of the hypotenuse to the adjacent side.
    Cotangent: Cotan is the ratio of the adjacent side to the opposite side.
  4. What are some of the real-life applications of trigonometry?
    Some real-life applications of trigonometry include calculating heights and distances in civil engineering. It also has uses in designing models in CAD/ AUTOCAD and navigation, criminology, and more.
  5. Is there any relation between the tangent and cotangent function?
    Yes, the tangent and the cotangent function are related to each other. Cotangent is the reciprocal value of the tangent and vice-versa.

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