# S.L. Loney Trigonometrical Ratios Solutions (Chapter 2)

SL Loney Plane Trigonometry Solutions for Chapter 2: Trigonometric Ratios is one of the best solution books that will assist you to easily crack competitive exams like IIT JEE. When you go through the solutions for Trigonometric Ratios, all your concepts and fundamentals on the chapter would become very clear. In this chapter, the topics covered are based on trigonometric ratios, limit to trigonometric equations, complementary angles, the relation between trigonometric ratios.

SL Loney Trigonometry Solutions for Trigonometric Ratios consist of 66 questions and 3 exercises. By practising these exercises, you will learn how to solve several trigonometric equations. A few important questions of the exercise are the ones based on angular value and proof for a trigonometric function. The questions might be hard and tricky but solving those questions will sharpen your mind for tough exams like JEE Advanced.

The experts at Instasolv have made it easier for you to solve all trigonometric ratios questions. Other than providing SL Loney exercise solutions, we have also made every effort to make all concepts of the chapter very clear. After going through these solutions, you can learn how to solve every trigonometric ratio question with tricks and tips. The simplicity of language used in the solution makes it easy for you to understand the subject matter very easily and rapidly. Besides you can also learn to manage time in exams more efficiently which is one of the best factors for qualifying exams.

## Important Topics for SL Loney Plane Trigonometry Solutions Chapter 2: Trigonometric Ratios

SL Loney Plane Trigonometry Solutions for Trigonometric Ratios consist of all basic concepts of all trigonometric ratios. Along with that, you will learn how to use those ratios for solving some equations and trigonometric ratios for certain angles. All the questions present in this book are a bit tricky and hard. But solving these would help you all your lacks in the field.

**Trigonometric ratios:** It is obtained from the sides of the right-angled triangle. There are six ratios namely sine, cosine, tangent, cotangent and secant. Trigonometric ratios are defined as the values of all trigonometric functions depending on the value of the ratio of sides in the right-angle triangle.

In a right angle triangle ABC

Sine of any angle is the ratio of the perpendicular side to the angle of the hypotenuse.

- sin θ = (Side opposite to ∠θ)/(Hypotenuse) = CB/CA

Cosine of an angle is called the ratio of the side adjacent to the angle of the hypotenuse.

- cos θ = (Side adjacent to ∠θ)/(Hypotenuse) = AB/AC

Tangent of an angle is the ratio of the side opposite to the angle to the side that is adjacent to that angle.

- tan θ = (Side opposite to ∠θ)/(Side adjacent to ∠θ) = CB/AB = sin ∠θ/cos ∠θ
- Cosecant is the inverse of sine.

cosec θ = 1/sin θ = (Hypotenuse)/ (Side Opposite to ∠θ) =AC/CB

- The inverse of cosine is secant.

sec θ = 1/cos θ = (Hypotenuse)/ (Side Opposite to ∠θ) = AC/AB

- Cotangent is the inverse of the tangent.

cot θ = 1/tan θ = (Side adjacent to ∠θ)/(Side opposite to ∠θ)= AB/CB

There exists a fundamental relation between trigonometric ratios of an angle.

sin^{2} θ + cos ^{2} θ = 1

tan ^{2} θ + 1 = sec ^{2} θ

1 + cot ^{2} θ = coc^{2 }θ

**Limits to the value of trigonometric equations**: In the equation sin ^{2 }θ + cos^{2} θ = 1, being squares are positive and the sum of their squares is unity. So, neither of them is greater than unity.

**Complementary angles**: Two angles are complementary when their sum is a right angle.

### Discussion of Exercises of SL Loney Plane Trigonometry Solutions Chapter 2: Trigonometric ratios

- In SL Loney Plane Trigonometry Solutions for Trigonometric Ratios, there are a total of 66 questions which is divided into three parts depending on various concepts of trigonometric ratios.
- In the first part, there are 35 questions where you are asked to prove certain equations based on the various trigonometric ratio equations and the relationship that exists between this ratio of an angle.
- In the second part, there are about 22 questions based on the limit to the trigonometric concepts. By applying the equations you can solve the questions.
- In the third section, there are 9 questions based on complementary angles and trigonometry ratios.

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