{"id":804994,"date":"2024-01-12T12:27:02","date_gmt":"2024-01-12T06:57:02","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=804994"},"modified":"2024-01-12T12:27:02","modified_gmt":"2024-01-12T06:57:02","slug":"exam-prep-trignometry-formulas","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/","title":{"rendered":"21 Trignometry Formulas for Competitive Exams\u00a0"},"content":{"rendered":"\n

One of the most important concepts to understand in the quantitative aptitude section<\/strong> is trigonometry. The study of triangles is basically what trigonometry is, where “trigon” stands for triangle and “metric” for measurement. Trigonometry deals with how a right-angled triangle’s angles and sides relate to one another and how to use this information to calculate distances and heights. Read our blog to go through the list of the most important maths trigonometry formulas that a student preparing for competitive exams should not miss.<\/p>\n\n\n\n\n\n\n

Firstly the trigonometry table can be used to answer the problems as it is a helpful and easy-to-understand resource. The trigonometry table for angles that are frequently used to solve problems is shown below:<\/p>\n\n\n\n

Angles (In Degrees)<\/strong><\/td>0\u00b0<\/strong><\/td>30\u00b0<\/strong><\/td>45\u00b0<\/strong><\/td>60\u00b0<\/strong><\/td>90\u00b0<\/strong><\/td>180\u00b0<\/strong><\/td>270\u00b0<\/strong><\/td>360\u00b0<\/strong><\/td><\/tr>
Angles (In Radians)<\/strong><\/td>0<\/strong><\/td>\u03c0\/6<\/strong><\/td>\u03c0\/4<\/strong><\/td>\u03c0\/3<\/strong><\/td>\u03c0\/2<\/strong><\/td>\u03c0<\/strong><\/td>3\u03c0\/2<\/strong><\/td>2\u03c0<\/strong><\/td><\/tr>
sin<\/td>0<\/td>1\/2<\/td>1\/\u221a2<\/td>\u221a3\/2<\/td>1<\/td>0<\/td>-1<\/td>0<\/td><\/tr>
cos<\/td>1<\/td>\u221a3\/2<\/td>1\/\u221a2<\/td>1\/2<\/td>0<\/td>-1<\/td>0<\/td>1<\/td><\/tr>
tan<\/td>0<\/td>1\/\u221a3<\/td>1<\/td>\u221a3<\/td>\u221e<\/td>0<\/td>\u221e<\/td>0<\/td><\/tr>
cot<\/td>\u221e<\/td>\u221a3<\/td>1<\/td>1\/\u221a3<\/td>0<\/td>\u221e<\/td>0<\/td>\u221e<\/td><\/tr>
cosec<\/td>\u221e<\/td>2<\/td>\u221a2<\/td>2\/\u221a3<\/td>1<\/td>\u221e<\/td>-1<\/td>\u221e<\/td><\/tr>
sec<\/td>1<\/td>2\/\u221a3<\/td>\u221a2<\/td>2<\/td>\u221e<\/td>-1<\/td>\u221e<\/td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Must Read: NDA Exam Syllabus 2024: Subject-wise Syllabus\ud83d\udc6e<\/strong><\/a><\/p>\n\n\n\n

21 Most Important Formulas in Trigonometry<\/h2>\n\n\n\n

Since many students find it challenging to memorize all of the formulas. It is very important to understand the basic formulas first, as these can be used to derive all other formulas. So are you excited to know what these fundamental identities of trigonometry are? If you’re new to trigonometry, or if you just need to revise your concepts, here are the most important maths trigonometry formulas you need to know:<\/p>\n\n\n\n

Basic Ratios<\/strong>

sin \u03b8 = Opposite Side\/Hypotenuse
cos \u03b8 = Adjacent Side\/Hypotenuse
tan \u03b8 = Opposite Side\/Adjacent Side
sec \u03b8 = Hypotenuse\/Adjacent Side
cosec \u03b8 = Hypotenuse\/Opposite Side
cot \u03b8 = Adjacent Side\/Opposite Side<\/td>		Reciprocal Identities<\/strong>

cosec \u03b8 = 1\/sin \u03b8
sec \u03b8 = 1\/cos \u03b8
cot \u03b8 = 1\/tan \u03b8
sin \u03b8 = 1\/cosec \u03b8
cos \u03b8 = 1\/sec \u03b8
tan \u03b8 = 1\/cot \u03b8
<\/td><\/tr>
Periodic Identities <\/strong>

sin (\u03b8 + 2\u03c0) = sin \u03b8
cos (\u03b8 + 2\u03c0) = cos \u03b8
tan (\u03b8 + 2\u03c0) = tan \u03b8<\/td>		Co-function Identities <\/strong>

sin (90\u00b0 – \u03b8) = cos \u03b8
cos (90\u00b0 – \u03b8) = sin \u03b8
tan (90\u00b0 – \u03b8) = cot \u03b8
<\/td><\/tr>
Sum and Difference Identities<\/strong>

sin (A + B) = sin A cos B + cos A sin B
cos (A + B) = cos A cos B – sin A sin B
sin (A – B) = sin A cos B – cos A sin B
cos (A – B) = cos A cos B + sin A sin B<\/td>		Double Angle Identities<\/strong>

sin 2\u03b8 = 2 sin \u03b8 cos \u03b8
cos 2\u03b8 = 2
cos\u00b2 \u03b8 – 1 or 1 – 2
sin\u00b2 \u03b8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Must Read: AFCAT Notification 2024<\/strong><\/a><\/p>\n\n\n\n

Solved Examples<\/h2>\n\n\n\n

Q1. Solve for x in the equation 2sin(x) – 1 = 0.<\/strong><\/p>\n\n\n\n

Given equation: 2sin(x) – 1 = 0<\/p>\n\n\n\n

Adding 1 to both sides: 2sin(x) = 1<\/p>\n\n\n\n

Dividing both sides by 2: sin(x) = 1\/2<\/p>\n\n\n\n

This implies that x is in the first and second quadrants, where sin(x) is positive.<\/p>\n\n\n\n

Using the fact that sin(30\u00b0) = 1\/2, we can write: x = 30\u00b0 or x = 180\u00b0 – 30\u00b0<\/p>\n\n\n\n

x = 30\u00b0 and x = 150\u00b0<\/p>\n\n\n\n

Q2. If cos(A) = -3\/5 and A is in the second quadrant, find sin(A) and tan(A).<\/strong><\/p>\n\n\n\n

Given, cos(A) = -3\/5<\/p>\n\n\n\n

Since A is in the second quadrant, sin(A) is positive. <\/p>\n\n\n\n

Using the Pythagorean identity sin\u00b2<\/strong> (A) + cos\u00b2<\/strong> (A) = 1<\/p>\n\n\n\n

sin\u00b2<\/strong> (A) + (-3\/5)\u00b2<\/strong>  = 1<\/p>\n\n\n\n

sin\u00b2<\/strong> (A) + 9\/25 = 1<\/p>\n\n\n\n

sin\u00b2<\/strong> (A) = 16\/25<\/p>\n\n\n\n

Taking the positive square root:<\/p>\n\n\n\n

sin(A) = 4\/5<\/strong><\/p>\n\n\n\n

tan(A) = sin(A)\/cos(A) = (4\/5)\/(-3\/5) <\/p>\n\n\n\n

tan (A)= -4\/3<\/strong><\/p>\n\n\n\n

Must Read: Algebra Formulas for GMAT Quantitative Reasoning Section<\/strong><\/p>\n\n\n\n

FAQS<\/h2>\n\n\n\n
What are the basic formulas of trigonometry?<\/strong>

Basic maths trigonometry formulas include the Pythagorean identity (sin\u00b2\u03b8 + cos\u00b2\u03b8 = 1), sum and difference identities, and the double angle formulas (e.g., sin(2\u03b8) = 2sin\u03b8cos\u03b8).<\/p> <\/div>

What are the 6 basic trigonometric functions?<\/strong>

The six basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions relate the angles of a right triangle to the ratios of its sides.<\/p> <\/div>

How do do class 10 trigonometry?<\/strong>

For class 10 trigonometry, start by understanding the basic trigonometric ratios (sin, cos, tan) and their reciprocal functions. Practice solving problems involving right triangles using these ratios, and gradually move on to more complex concepts like trigonometric identities.<\/p> <\/div> <\/div>\n\n\n\n

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This was all about the \u201c Trignometry Formulas <\/strong>\u201d. For more such informative blogs, check out our Study Material Section<\/strong><\/a>, or you can learn more about us by visiting our Indian exams<\/strong><\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"One of the most important concepts to understand in the quantitative aptitude section is trigonometry. 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I'm a content writer who turns complex ideas into clear, engaging stories. Think of me as your translator, taking expert knowledge and making it interesting and relatable for everyone.","url":"https:\/\/leverageedu.com\/discover\/author\/amisha\/"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/#faq-question-1705128951981","position":1,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/#faq-question-1705128951981","name":"What are the basic formulas of trigonometry?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"Basic maths trigonometry formulas include the Pythagorean identity (sin\u00b2\u03b8 + cos\u00b2\u03b8 = 1), sum and difference identities, and the double angle formulas (e.g., sin(2\u03b8) = 2sin\u03b8cos\u03b8).","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/#faq-question-1705128962712","position":2,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/#faq-question-1705128962712","name":"What are the 6 basic trigonometric functions?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"The six basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions relate the angles of a right triangle to the ratios of its sides.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/#faq-question-1705128983455","position":3,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-trignometry-formulas\/#faq-question-1705128983455","name":"How do do class 10 trigonometry?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"For class 10 trigonometry, start by understanding the basic trigonometric ratios (sin, cos, tan) and their reciprocal functions. Practice solving problems involving right triangles using these ratios, and gradually move on to more complex concepts like trigonometric identities.","inLanguage":"en-US"},"inLanguage":"en-US"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/804994","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/users\/113"}],"replies":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/comments?post=804994"}],"version-history":[{"count":0,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/804994\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media\/804997"}],"wp:attachment":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media?parent=804994"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/categories?post=804994"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/tags?post=804994"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}