RS Aggarwal Class 10 Chapter 11 Solutions (T-Ratios of Some Particular Angles)
RS Aggarwal Class 10 Maths Solutions for Chapter 11 ‘T-Ratios of Some Particular Angles’ are available here for you to give you a brief overview of the different problems related to the topic. In this chapter of RS Aggarwal Class 10 Maths Solutions, you will study different concepts on Trigonometric ratios of some particular angles such as T-ratios of some particular angles introduction, T-ratios of different angles (30 degrees, 45 degrees, and 60 degrees), axioms for T-ratios of 0 and 90 degrees, etc.
Chapter 11 RS Aggarwal Solutions for Class 10 are composed of only 1 exercise that contains 27 questions. These sets of questions created are of varying difficulty levels and can be referred to you to master the trigonometric-ratios. All the questions of the chapter are based on the latest CBSE Class 10 Maths syllabus. Their solutions will help you prepare the chapter thoroughly so that you can handle all kinds of problems related to trigonometric ratios in the board exams.
RS Aggarwal’s solutions are an authentic source for you to do the quick revision of the topic. Our team of experts has provided the simplest and easy approach to solve the problems related to the topic. These RS Aggarwal’s solutions are beneficial for you to get a grip over solving the difficult questions. We suggest you have this RS Aggarwal textbook for the better preparation of your upcoming exams.
Important Topics of RS Aggarwal Class 10 Maths Solutions Chapter 11: T-Ratios of Some Particular angles
As you know trigonometric ratios are an important topic in class 10. Let us see its applications for some specific angles:
Trigonometric-Ratios for 45 Degrees:
Let us consider a right-angled triangle ΔABC-
If in a right angle triangle ΔABC-
If angle ∠A is 45 degree , then the other angle ∠C will also be 45 degree i.e ∠A= ∠C
Therefore, BC = AB
Suppose , BC=AB = a
Now using Pythagoras theorem for this triangle-
(AC)^{2}= (AB)^{2} + (BC)^{2}
(AC)^{2} = (a)^{2} + (a)^{2}
= 2.(a)^{2}
AC = a √2
Now using the definitions of trigonometric-ratios:
Here θ = 45 degree
sinθ = perpendicular / hypotenuse
= BC/ AC
= a/a √2
= 1/√2
cosecθ = 1/ sinθ
= √2
cosθ = base / hypotenuse
= AB/ AC
= a/a √2
= 1/√2
Secθ = 1/ cosθ
= √2
tanθ = perpendicular/ base
= BC/ AB
= a/a
= 1
Cotθ = 1/ tanθ
= 1
In the case of trigonometric ratios for 30 and 60 degrees, we need to take an equilateral triangle. Using properties of it we will be able to find the trigonometric ratios for 30 and 60 Degrees.
Relation Between Trigonometric Ratios
Let us see the relationship between trigonometric ratios-
- Cosec θ = 1/ sin θ
- sec θ = 1/cos θ
- tan θ = sin θ/cos θ
- cot θ = cos θ/sin θ=1/tan θ
Ranges of Trigonometric Ratios-
Let’s have a look at ranges of trigonometric ratios-
- 0≤sinθ≤1
- 0≤cosθ≤1
- 0≤tanθ<∞
- 1≤secθ<∞
- 0≤cotθ<∞
- 1≤cosecθ<∞
Standard Values of Trigonometric Ratios-
Angle |
0° |
30° |
45° |
60° |
90° |
sin A |
0 |
1/2 |
1/√2 |
√3/2 |
1 |
cos A |
1 |
√3/2 |
1/√2 |
1/2 |
0 |
tan A |
0 |
1/√3 |
1 |
√3 |
not defined |
cosec A |
not defined |
2 |
√2 |
2/√3 |
1 |
sec A |
1 |
2/√3 |
√2 |
2 |
not defined |
cot A |
not defined |
√3 |
1 |
1/√3 |
0 |
Exercise Discussion of RS Aggarwal Class 10 Maths Solutions Chapter 11: T-Ratios of Some Particular angles
- RS Aggarwal Solutions for Class 10 Chapter 11 has only one exercise that contains 27 problems, arranged beautifully which covers almost all the concepts of the chapter extensively.
- Questions 1 to 9 are of evaluation types at which you need to evaluate the value from the given trigonometric relations. For instance, one question is about sin 60° cos 30° + cos 60° sin 30°. Almost all the questions are of the same type.
- The next type of questions is of the type at which you need to prove that LHS is equal to RHS. These questions are quite interesting and sometimes tricky also but are very important to your exam point of view.
- The next set of questions is of the type where you need to find the length of sides of a right-angled triangle. These questions are quite tough compared to others. For solving these questions you need to have a better grip over trigonometric ratios and identities.
Benefits of RS Aggarwal Class 10 Maths Solutions Chapter 11: T-Ratios of Some Particular angles by Instasolv
- RS Aggarwal Solutions of Class 10 Chapter 11 is an authentic source for you to practice questions. The information provided in the solutions helps you cover the concepts of the chapter easily.
- Our subject matter experts have reviewed all the questions of the chapter based on the latest CBSE syllabus.
- Taking guidance from these solutions would be highly beneficial to help you perform well in both school and competition level exams.