Watch the second video session on “Introduction To Trigonometry” for Class Xth – concepts and solved questions
Introduction To Trigonometry – Class X – Part 2
1. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). It is the study of relationships between the sides and angles of a triangle.
2. Early astronomers used it to find out the distances of the stars and planets from the Earth.Today, most of the technologically advanced methods used in Engineering and Physical Sciences are based on trigonometrical concepts.
Steps to find the trigonometric ratios with respect to an angle (say A) in a right angled triangle:
a. Keep triangle in such a way so that angle A is in the base (along with the 90 degree angle).
b. Identify the “perpendicular” (p), “base” (b) and hypotenuse (h) sides. Usually two of the sides are given; the unknown can be calculated using Pythagoras Theorem.
c. Find out the required trigonometric ratio. (Refer to the video to find out the shortcut to remember the six trigonometric ratios.)
NCERT Exercise 8.1 Q5-9 Solved
5. Given sec θ =13 / 12, calculate all other trigonometric ratios.
6. If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.
7. If cot θ =7 / 8
(i)(1+ sinθ) (1 – sinθ )/(1+ cosθ) (1 – cosθ )
(ii) (cotθ)(cotθ) [Read as cot square theta]
8. If 3 cot A = 4, check whether [1-(tanA)^2]/[1+(tanA)^2] = (cosA)^2 – (sinA)^2
9. In triangle ABC, right-angled at B, if tan A =1/(root3), find the value of
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C