## Some Basic Concepts in Chemistry for JEE (2)

This chapter in itself is a combination of many other chapters. Although rarely direct questions are asked from this chapter, yet it finds endless applications in calculus and algebra, so basically it serves as a “tool” to solve problems of other topics.

**Trigonometric functions:**This chapter introduces the definition of the 6 T-ratios as the ratio of the sides of a right angled triangle. Further, the relationship between the T-ratios is taught. Then come the 3 fundamental identities:

**sin**^{2}Ɵ + cos^{2}Ɵ = 1**1 + tan**^{2}Ɵ = sec^{2}Ɵ**1 + cot**^{2}Ɵ = cosec^{2}Ɵ

These are the most important identities of trigonometry and can be derived from Pythagoras theorem easily. A number of questions can be solved by writing **1 - cos ^{2}Ɵ **instead of

**sin**

^{2}Ɵ.There is a good technique to memorize the sign of the T-ratios.

Quadrant -> |
I |
II |
III |
IV |

t-ratios which are positive |
All |
sinƟ cosecƟ |
tanƟ cotƟ |
cosƟ secƟ |

This table can be memorised with the help of the phrase:

**Add** **Sugar To Coffee**

**(This can also be added as a concept map / aid to memory)**

A useful thing to solve problems is to note that the range of is (-∞ , -2] U [2 , ∞). This fact often helps.

The T-ratios of allied angles must be thoroughly covered.

Another important point to note is that trigonometric functions are periodic. The periodicity of the trigonometric functions is an important property and has wide applications in mathematics and engineering physics. Students should be able to make graph of the functions keeping the periodicity in mind.

One final thing that is expected is that students should be able to integrate the above ideas to prove various identities involving trigonometric functions. They should be able to use algebra in trigonometry and trigonometry in algebra and calculus.

**Compound and multiple angles:**This chapter begins with the most elementary formulae of sin(A ± B), cos(A ± B) and tan(A ± B) in terms of sin A, cos A, tan A and sin B, cos B, tan B. Another important formula which is sometimes asked is that of tan(A + B + C). Students should**memorize the above formulae by heart.**

Further introduced are the most important “A, B” formulae and “C, D” formulae

**2 sin A cos B = sin (A + B) + sin (A – B)****2 cos A sin B = sin (A + B) - sin (A – B)****2 cos A cos B = cos (A + B) + cos (A – B)****2 sin A sin B = cos (A - B) - cos (A + B)****à (note that this formula is a bit different)****sin C + sin D = 2 sin ((C + D) / 2) cos ((C + D) / 2) (please format this correctly to look mathematical – or rather make it as an image or a concept map)****sin C - sin D = 2 cos ((C + D) / 2) sin ((C + D) / 2)****cos C + cos D = 2 cos ((C + D) / 2) cos ((C + D) / 2)****cos C - cos D = 2 sin ((C + D) / 2) sin ((C + D) / 2)**- T-ratios of 2A in terms of those of A
- T-ratios of 3A in terms of those of A
- T-ratios of submultiple angles

Next taught are the most important T-ratios of multiple and submultiple angles:

Rest this entire chapter is all about applying the correct formula at the correct place. Students should practice enough questions so that these formulae get embedded in their minds.

**Trigonometric equations:**This is s straightforward and a simple chapter. One of the best chapters in trigonometry. A number of questions are asked in JEE from this chapter and the questions are fairly direct. Students are expected to solve standard forms of trigonometric equations that occur frequently in engineering. Most of this chapter is the “tool” part and is widely used.

To summarise, most students find trigonometry boring because of so many formulae involved in it. But those aiming for good ranks in competitive exams should not miss even a single formula. The paper setters of competitive exams are well aware of what students generally overlook and so they deliberately introduce questions from those concepts.

For trigonometry, a one liner would be – “*practice makes a human perfect”*

## Playing your strengths - How to capitalize on your strong subject areas to score more in GATE

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[...]## When is the ideal time to begin serious preparation for GATE?

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