{"id":8975,"date":"2016-03-07T14:23:01","date_gmt":"2016-03-07T08:53:01","guid":{"rendered":"https:\/\/www.askiitians.com\/blog\/?p=8975"},"modified":"2016-03-07T14:23:01","modified_gmt":"2016-03-07T08:53:01","slug":"top-5-trigonometrc-properties-used-solving-95-questions","status":"publish","type":"post","link":"https:\/\/www.askiitians.com\/blog\/top-5-trigonometrc-properties-used-solving-95-questions\/","title":{"rendered":"Top 5 Trigonometrc properties used for solving 95% questions"},"content":{"rendered":"

Once there was a boy. His name was Cess<\/b>. He had a friend whose name was Suc<\/b>. They were best of the friends till grade 10. But one day they fought for numbers. From that day onwards, they started parting their ways. JEE was their aim and both of them had a weak point. “Trigonometry “.<\/p>\n

\"38\"<\/a><\/p>\n

\u00c3\u201a\u00c2\u00a0A teacher from the school somehow had this information. He devised a plan to make them successful and friends again. He collected golden properties of trigonometry which will solve 95% of questions of JEE.\u00c3\u201a\u00c2\u00a0The <\/span>teacher\u00c3\u201a\u00c2\u00a0<\/span>called them to his home for helping them. But he called them one after the other. He gave names to 6 golden properties in a unique fashion. You want to know what he did???<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
\n

Unique code<\/span><\/b><\/p>\n<\/td>\n

\n

Property<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

C2<\/span><\/b><\/p>\n<\/td>\n

\n

Half and Compound Angle formula<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

S1<\/span><\/b><\/p>\n<\/td>\n

\n

Combination formula tan (A\u00c3\u201a\u00c2\u00b1B)<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

E1<\/span><\/b><\/p>\n<\/td>\n

\n

tan-1 <\/sup>x = <\/span><\/b>\u00c3\u2018\u00c2\u00b2<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

U1<\/span><\/b><\/p>\n<\/td>\n

\n

Conversion and Combination Formula<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

C2<\/span><\/b><\/p>\n<\/td>\n

\n

Finding out roots<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n

\n

S2<\/span><\/b><\/p>\n<\/td>\n

\n

\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0\u00c3\u201a\u00c2\u00a0 Basic Simplification<\/span><\/b><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

C2Half and Compound Angle formula\u00c3\u201a\u00c2\u00a0<\/span><\/span><\/b>This was explained\u00c3\u201a\u00c2\u00a0<\/span>process<\/span>.<\/span><\/span><\/span><\/b><\/p>\n

In this, the teacher said,\u00c3\u00a2\u00e2\u201a\u00ac\u00c2\u009dIt is the class of formulas in which the question will be dealing with <\/span>\u00c3\u2018\u00c2\u00b2<\/span>, 2<\/span>\u00c3\u2018\u00c2\u00b2<\/span> ,<\/span>\u00c3\u2018\u00c2\u00b2<\/span>\/2 and you have to convert them into their respective half angles to find out the answer \u00c3\u00a2\u00e2\u201a\u00ac\u00c2\u009d.<\/span><\/p>\n

\"39\"<\/a>These basic formulas were catered in numerous question which are given below along with the year in which they showed up in the examination.<\/span><\/p>\n

\"41\"\"42\"<\/a>Summing this up he said just analyze the consistency of the questions that use this basic property in order to get to the answer.Master yourself in this and you will be the happiest soul coming out of exam if any trigonometry question shows up.<\/span><\/p>\n

S1 <\/span><\/b>Combination formula tan (A\u00c3\u201a\u00c2\u00b1B)\u00c3\u201a\u00c2\u00a0This was explained to Suc
\n<\/span><\/b><\/p>\n

This formula is used directly or indirectly in the majority of the questions that have come in all the different competitive exams. Let\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s see all those questions which popup taking this property as the base which will be used in order to solve it.<\/span><\/p>\n

\"43\"<\/a><\/p>\n

\"44\"\"45\"<\/a>E1 <\/span><\/b>tan-1 <\/sup>x = <\/span><\/b>\u00c3\u2018\u00c2\u00b2 <\/span><\/b>this was explained to Cess.<\/span><\/b><\/p>\n

\u00c3\u201a\u00c2\u00a0A very simple yet very effective property which will help in across all the inverse trigo questions. You just have to assume any of the inverse functions as equal to angle and then move ahead with that simplification using the help of right angle triangle.With this piece of information you can easily achieve all the other trigonometric ratios and can solve the question .These questions have also shown their periodicity in the JEE papers over the years.Let\u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u201e\u00a2s see some of them.\"\"<\/b><\/span><\/p>\n

 <\/p>\n

U1 <\/span><\/b>Conversionand Combination Formula\u00c3\u201a\u00c2\u00a0<\/span><\/b>This was explained to Cess.<\/span><\/b><\/b><\/p>\n

Representing one ratio in terms of other is the most interesting part of trigo. Inter-conversion always helps in going for easier and faster solutions. Question setter also accept this fact which gets acknowledged by the kind of questions they ask on this pattern. Along with conversion, combination also has its niche in JEE. You need to learn how to use inverse for +ve or \u00c3\u00a2\u00e2\u201a\u00ac\u00e2\u20ac\u0153ve values, how to convert tan into cos, sin and other ratios, etc.<\/b><\/span><\/p>\n

Understand the conversion rather than just remembering it because IIT will play games with you if you just remember it and will make you look like a FOOL by giving twisted Questions.Below written are the questions with years in which they popped up.<\/b><\/span><\/p>\n

\"47\"\"48\"<\/a>C2 Finding out roots\u00c3\u201a\u00c2\u00a0<\/span><\/b>This was explained to Suc.<\/span><\/b><\/p>\n

When you equate two ratios what is the general solution that you will get. One of the pillars of trigonometric equations which everyone must know if they are trying to excel themselves in this part of maths. Again I would want you to focus on the procedure rather than the answer. JEE always want rational minds who can think up and process information to get to an optimized result with least possible input.<\/span><\/p>\n

Eg: sin<\/span>\u00c3\u2018\u00c2\u00b2<\/span> = sin<\/span>\u00c3\u017d\u00c2\u00b1<\/span>, tan<\/span>\u00c3\u017d\u00c2\u00b1<\/span> = tan<\/span>\u00c3\u2018\u00c2\u00b2<\/span> n so on..<\/span><\/p>\n

\"49\"\"50\"\"52\"<\/a><\/p>\n

\"54\"<\/a>S2 Range of sin-1 <\/sup>x <\/span><\/b>This was explained to Suc.<\/span><\/b><\/p>\n

This part deals with the most basic understanding of the inverse trigonometric ratios. It will only come once you are done with the exact understanding of inverse functions. If you have any doubts in inverse trigo you can understand basic inverse functions and then revisit this part again.<\/b><\/span><\/p>\n

\"55\"<\/a>After this training, teacher explained them that for getting through JEE they have to\u00c3\u201a\u00c2\u00a0 mix up what they have learnt from him. But on condition of not mixing up numbers Without much of ego they combined what they have learnt with super effort.<\/span><\/p>\n

\"56\"<\/a><\/p>\n

\"57\"<\/a><\/p>\n

Goes as SUCCESS<\/b>. Now if you also want to be like two friends and want to be as successful as CESS<\/b> n SUC<\/b> are. Use properties and sail through the competition.<\/span><\/p>\n

Best of Luck!!!<\/span><\/p>\n

This whole episode is part of a ral life incident how my teacher helped me out in becoming successful. I, Sourabh Singh from AskIITians is one of the two boys.It worked for me & I am sure it will work for you too. For more such interesting stuff you must visit.<\/span><\/p>\n

Straight Lines<\/strong><\/span><\/a><\/p>\n

Probability<\/strong><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Once there was a boy. His name was Cess. He had a friend whose name was Suc. They were best of the friends till grade 10. But one day they fought for numbers. From that day onwards, they started parting their ways. JEE was their aim and both of them had a weak point. “Trigonometry […]<\/p>\n","protected":false},"author":2,"featured_media":8994,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-8975","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/posts\/8975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/comments?post=8975"}],"version-history":[{"count":0,"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/posts\/8975\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/media\/8994"}],"wp:attachment":[{"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/media?parent=8975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/categories?post=8975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.askiitians.com\/blog\/wp-json\/wp\/v2\/tags?post=8975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}