The document discusses trigonometry and trigonometric ratios. It defines trigonometry as the study of triangles and trigonometric ratios as ratios of sides of a right triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are the ratios of the opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent sides, respectively. Examples are given to demonstrate calculating trigonometric ratios using the properties of right triangles. Common mistakes made by students are also discussed.

4. A trigonometric ratio is a ratio of the lengths of two sides in a right triangle. TRIGONOMETRIC RATIO

5. Three basic trigonometric ratios: sine cosine tangent each of which is the ratio of one side to another. .

12. opposite adjacent A B C Hypotenuse Base Perpendicular

13. S C T P B P H H B Sin P H Cos B H Tan P B

14. 6 8 10 A B C (P) (B) (H)

15. Identify perpendicular , hypotenuse and base in relation to angle C in given fig. A B C

18. Example 1: Finding the Value of Trigonometric Ratio sin A, cos A, tan A,cosec A,sec A and cot A . A B C 17 15 8

19. sin A, cos A, tan A,cosec A,sec A and cot A . Sin A Cos A Tan A solution A B C 17 15 8

20. A B C 17 15 8

21. Find the values of all the trigonometric ratios of  . 4 3 ? Pythagoras Theorem: (3) ² + (4)² = c² 5 = c 5

22. Example 2:If tan A=4/3 then calculate sinA.cosA SOLUTION A B C Let us first draw a right ABC As we know 3k 4k Therefore BC=4k,AB=3k, where k is any positive number. Now,by using Pythagoras theorem we have AC 2 = AB 2 + BC 2 =(3K) 2 +(4K) 2 =9K 2 + 16K 2 AC 2 =25K 2 AC=5K

23. A B C 4k 3k 5K Answer= 12/25

24. Students tend to make simple mistakes by mislabeling the perpendicular and base To overcome this mistake first determine the Hypotenuse. The side opposite to acute angle under Consideration is the perpendicular. COMMON ERROR ALERT

26. In ABC right angle at B, if calculate all other trigonometric ratios. QUESTION 2