Trigonometry – the branch of mathematics, dealing with six T–ratios is interesting. While it is a game for some to play with, it is head–scratching for others. But a little care can ward off all the unfounded fears of students, is opined by me. In CBSE – 2010 Class X examination, trigonometry carries a weightage of 12 marks out of 80. It includes one question of 1 mark, one question of 2 marks, one question of 3 marks and 1 question of 6 marks. The important topics in CBSE board examinations which attract the attention of the examiner for setting of questions are:– 1. relation among six ratios; 2. values of T--ratios of standard angles; 3. complementary angle relations; 4. trigonometrical identities; and 5. heights and distances. Taking topic wise, the questions asked from this section are very simple. Generally students memorize only one relation viz. (Sin)2 A + (Cos)2 A = 1 leaving the other two, which are equally important for solving a good number of questions. For CBSE – 2010 exams, students should practice some questions involving the usage of these two relations, which will certainly help to build confidence in them. One question is based on the value of T–ratios of standard angle & complementary angle relations. Students get confused in memorizing complementary angle relations. An easy way is:
“Attach ‘Co’ to T–ratios without ‘Co’ & remove ‘Co’ from T–ratios with ‘Co’.” e.g. Sin(90 – A) = Cosine A. Cosine (90 – A) = Sin A
To solve such questions locate the pairs of complementary angle T–ratios. For example, for, 10 degree, 80 degree, 20 degree, 70 degree, 25 degree, 65 degree, etc. Change one of the T–ratios in terms of complementary angle. The final result thus obtained, will automatically cancel out, leaving the question in the most simplified form.
Here 70 degree, 20 degree; 36 degree, 54 degree; 43 degree, 47 degree; 10 degree, 80degree; 40degree, 50 degree make complementary pairs. Take note that only one angle is to be changed and not both. This method will work to solve the sum without any difficulty.
For trigonometrical identities, two types of questions are asked; one involving T–ratios other than Sin A + Cos A ; and the other involving questions with T–ratios within under–roots. For the first type of questions change T–ratios to Sin A + Cos A and solve them. For the second type of questions, rationalise the denominator, which will further simplify the question.
The most challenging portion for students in CBSE exams are the heights & distances question. To solve this question, the student should draw the diagram correctly keeping in view the various parameters given in the question. Most of the times, it is easy to find height/distance by using T–ratio “Cot A”. It makes the question simple and error–free. Secondly, equate the quantified relations to get results.
For questions involving reflection of cloud in lake water, keep in mind that image formed in water will be as far behind as the distance of cloud from lake water.
No student in CBSE exams 2010, aiming to score 80 marks can afford to ignore trigonometry. Anyways, it is not difficult to attain expertise if the questions are tried carefully keeping in mind the above suggestive steps.