Students who wish to join IIT for engineering should crack the JEE Main and JEE Advanced exams. In 2022, the JEE Main will be conducted in June and July. One needs determination, hard work and proper planning to crack the JEE exams. Students are recommended to prepare and plan accordingly so that they can ensure a seat at IIT.

Trigonometric functions and their applications are very important from an exam point of view.

Students can expect 2-3 questions from this topic for any entrance exam. **Trigonometry** has many formulas and identities which have to be learnt byheart. Students are advised to byheart the important formulas, identities and tricks of trigonometric functions and inverse trigonometric functions. They should have the conceptual clarity of this topic so that they can easily apply the formulas where required. In this article, we will discuss important topics to learn in trigonometric ratios, applications, etc.

## Important Things to Learn

Following are the very important things which students should definitely learn in trigonometric functions.

- Trigonometric identities
- Half angle formulas
- Reciprocal identities
- Periodicity identities
- Sum and difference identities
- Inverse trigonometric formulas

## Applications of Trigonometry

We use trigonometric relations and identities to solve heights and distances problems. It is used in architecture and construction. Trigonometric functions and formulas are used in astronomy to determine the distance between planets or stars. It is also used in physics and GPS navigation systems. It is also used in criminology. Marine biologists use trigonometric functions to determine the depth of sunlight that affects algae in photosynthesis. They estimate the size of marine animals such as whales by using the trigonometric function and mathematical models. It is also used in navigation, satellite systems and the making of maps.

Let us have a look at an example of a trigonometric problem.

Example: Find the value of M, if M = sin (π/18) sin (5π/18) sin (7π/18).

Solution:

- Given M = sin (π/18) sin (5π/18) sin (7π/18)
- We know π/18 = 180
^{0}/18 = 10^{0}, 5π/18 = 50^{0}, 7π/18 = 70^{0}. - So, M = sin 10
^{0}sin 50^{0}sin 70^{0} - = ½((cos (50
^{0}– 10^{0}) – cos (50^{0}+ 10^{0}))sin 70^{0} - = ½ (cos 40
^{0}– cos 60^{0})sin 70^{0} - = ½ cos 40
^{0}sin 70^{0}– ¼ sin 70^{0} - = ¼ [ sin 110
^{0}+ sin 30^{0}] – ¼ sin 70^{0} - = ¼ sin (180
^{0}– 70^{0}) + (¼ )(½) – ¼ sin 70^{0} - = ¼ sin 70
^{0}+ (¼ )(½) – ¼ sin 70^{0} - = 1/8.

So, the value of M is 1/8.

### Integration of trigonometric functions

Finding the integral of trigonometric and inverse trigonometric functions is a topic of great importance as far as the JEE exam is concerned. Students should also learn the formulas of **integration** of trigonometric functions. It will be very easy for them if they are thorough with the formulas when cracking problems. It will also help them to save time during the exam. Students can easily download PDFs of trigonometric formulas, solved question papers, important notes, etc., for free. Many websites are providing these types of learning resources which help students to take their learning to the next level.

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