{"id":335,"date":"2017-07-19T12:57:09","date_gmt":"2017-07-19T07:27:09","guid":{"rendered":"http:\/\/ibelitetutor.com\/blog\/?p=335"},"modified":"2023-08-14T12:50:42","modified_gmt":"2023-08-14T07:20:42","slug":"mathematics-tutors","status":"publish","type":"post","link":"http:\/\/ibelitetutor.com\/blog\/mathematics-tutors\/","title":{"rendered":"How to solve basic problems in trigonometry?(concept-2)"},"content":{"rendered":"

Mathematics tutor<\/h2>\n

IB Mathematics Tutor<\/a><\/strong> give great importance to Trigonometry<\/p>\n

Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships between the sides and angles of a triangle. Word trigonometry was originated from the Greek word, where, \u2018TRI<\/strong>\u2018 means\u00a0Three<\/em>,\u00a0\u2018GON<\/strong>\u2018 means\u00a0sides<\/em>\u00a0and the\u00a0\u2018METRON\u2019<\/strong>\u00a0means\u00a0to\u00a0measure.\u00a0<\/strong>It’s an ancient and probably the most widely used branch of Mathematics.<\/p>\n

For basic learning, Mathematics tutor divide trigonometry in two-part:-<\/p>\n

1 Trigonometry based on right triangles<\/p>\n

1 Trigonometry based on non-right triangles.<\/p>\n

In this post, we will discuss problems based on trigonometric ratios of a few specific angles like 0\u00b0,30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0. <\/strong>Mathematics tutor use different tricks to form this table. I will discuss my tricks in a separate post<\/p>\n

<\/p>\n

Concept-2<\/span><\/p>\n

In a trigonometric problem, If we are given a trigonometric ratio with a specific angle, we will first put the value of that ratio from the above table and do simplification. Simplification is usually based on L.C.M and rationalization.<\/span><\/p>\n

Example-1 Find the value of 4\/3 tan\u00b260\u00b0 + 3 cos\u00b230\u00b0 – 2 sec\u00b230\u00b0 – 3\/4 cot\u00b260\u00b0<\/strong><\/p>\n

Solution:\u00a0\u00a04\/3 tan\u00b260\u00b0 + 3 cos\u00b230\u00b0 – 2 sec\u00b230\u00b0 – 3\/4 cot\u00b260\u00b0<\/p>\n

<\/div>\n
=4\/3(\u221a3)\u00b2+3(\u221a3\/2)\u00b2-2(2\/\u221a3)\u00b2-3\/4(1\/\u221a3)\u00b2<\/div>\n
<\/div>\n
=4\/3(3)+3(3\/4)-2(4\/3)-3\/4(1\/3)<\/div>\n
<\/div>\n
=4+9\/4-8\/3-1\/3<\/div>\n
<\/div>\n
=4+9\/4-3<\/div>\n
<\/div>\n
=16+9-12\/3<\/div>\n
=13\/3<\/div>\n
<\/div>\n
\n

Example-2\u00a0<\/b>If A = 60\u00b0 and B = 30\u00b0, verify sin (A – B) = sin A cos B – cos A sin B<\/strong><\/p>\n

Solution:<\/b><\/p>\n

L.H.S.<\/strong> = sin (A – B)<\/p>\n

= sin (60\u00b0 – 30\u00b0)<\/p>\n

= sin 30\u00b0<\/p>\n

= \u00bd<\/p>\n

R.H.S.<\/strong> = sin A cos B – cos A sin B<\/p>\n

= sin 60\u00b0 cos 30\u00b0 – cos 60\u00b0 sin 30\u00b0<\/p>\n

=\u00a03<\/span><\/span>\u221a<\/span>2<\/span><\/span>\u00d7<\/span>3<\/span><\/span>\u221a<\/span>2<\/span><\/span>\u2212<\/span>1<\/span>2<\/span><\/span>\u00d7<\/span>1<\/span>2<\/span><\/span><\/span><\/span><\/span><\/p>\n

= \u00be – \u00bc<\/p>\n

= 2\/4<\/p>\n

= \u00bd<\/p>\n

Therefore, L.H.S. = R.H.S. (Proved)<\/p>\n

To get a better understanding of the concept you should check all my posts of Mathematics tutor series. you can check them by clicking on the links given below<\/p>\n

First post- concept one<\/span><\/h4>\n

Second post- concept two(current\u00a0post)<\/span><\/h4>\n

Third post -Concept three<\/span><\/h4>\n

Fourth post -Concept four<\/span><\/h4>\n<\/div>\n

\"ib<\/p>\n\n

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    <\/div>\n<\/form>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"

    Mathematics tutor IB Mathematics Tutor give great importance to Trigonometry Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships between […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-335","post","type-post","status-publish","format-standard","hentry","category-cbse-tutors"],"_links":{"self":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/posts\/335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/comments?post=335"}],"version-history":[{"count":0,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/posts\/335\/revisions"}],"wp:attachment":[{"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/media?parent=335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/categories?post=335"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ibelitetutor.com\/blog\/wp-json\/wp\/v2\/tags?post=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}