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S.L. Loney Trigonometric Function Solutions (Chapter 5)

SL Loney Plane Trigonometry Solutions for Chapter 5 ‘Trigonometric Functions’ are prepared with the sole purpose to help you be capable enough to crack exams like JEE and NEET. Trigonometry is a branch of mathematics mainly focused on the relationship between the angles and sides of a triangle. In this chapter of SL Loney Trigonometry Solutions, you will learn the definition of trigonometric functions, and how to find the values for different trigonometric functions of any angle in terms of. Further, in this chapter, you will also learn to find side length and angle measure using trigonometric functions.

Trigonometric Functions of SL Loney Plane Trigonometry contains 1 exercise with 38 questions. In these questions, you are asked to express Trigonometric ratios of various angles. Additionally, our solutions for Trigonometric Functions will help you learn useful relationships among different trigonometric functions. Few fundamental identities and formulas are the major part of the chapter which is essential to understand to solve the exercise questions.

The beneficial part of our SL Loney solutions for Trigonometric Functions is that our subject matter experts have gathered all the topics efficiently and have executed the theorems in a simpler manner. All the solutions are in accordance with the latest JEE Maths syllabus and exam pattern so as to help you in easy preparations. Every solution for Trigonometric Functions is checked at various levels ensuring their 100% accuracy and precision.

Important Topics for SL Loney Plane Trigonometry Solutions Chapter 5: Trigonometric Functions

The main part of the chapter is to learn Trigonometric Functions of any angles of any size or shape. Some Trigonometric ratios of an angle are -, (90- ), (90+ ), (180- ) and (360- ).

Trigonometric Ratios of an Angle (-)

In the above geometric triangle, OMP and OMP` are right angles. Also, the magnitude of the angles MOP and MOP` are the same and OP and OP` are equal.

Here, the magnitude of angle AOP and AOP` are the same. So, angle AOP` is denoted by . Therefore, we have

sin(-)        =      MP/ OP`    =     – MP/OP   =      -sin

cos(-)       =       OM/OP`    =      OM/OP    =     cos

tan(-)        =      MP`/OM    =    – MP/ OM  =     -tan

cot(-)        =      OM/MP`    =      OM/ -MP =     -cot

cosec(-)    =      OP`/ MP`   =      OP/-MP   =    -cosec

Sec(-)       =      OP`/OM     =      OP/OM    =     sec

Trigonometric Ratios of the angle (90)

Here the angle AOP` is 90-

By taking OP` equal to OP, P`M` and PM is drawn perpendicular to OA. Similarly, P`N` is drawn perpendicular to OB

As angle AOP and BOP` are equal, we get

Thus, we have

sin( 90- )     =    OM/OP   =   cos

cos( 90- )    =     MP/OP   =   sin

tan( 90- )     =    OM/MP  =   cot

cos( 90- )    =     MP/OM  =   tan

tan( 90- )     =    OP/MP    =   cosec

cosec( 90- ) =     OP/OM   =  sec

Trigonometric ratios of the angle  (90+ )

Let AOP =

When OP` is equal to OP, we draw PM and PM` perpendicular to AO.

As POP` is the right angle, the sum of MOP and M`OP` is a right angle.

Therefore, MOP=90 – P`OM` = OP`M`

Finally, we have Trigonometric Ratios of (90+)

sin(90+)    =   OM/OP    =   cos

cos)   =   -MP/OP   =   -sin

tan(90+)    =   OM/-MP  =  -cot

cot(90+    =   -MP/OM  =  -tan

sec(90+     =   OP/-MP  =  -cosec

Cosec(90+) =  OP/OM  =    sec

Supplementary Angles

When the sum of two angles is equal to two right angles it is said that those angles are supplementary. The supplement of any angle  = 180 -.

Trigonometric ratios of (180)

Here, the angle AOP` is 180-

MOP and M`OP` are equal. So, OM and OM` are equal in magnitude.

So we have,

sin(180- )        =  MP/OP    =    sin

cos(180- )       =  -OM/OP   =  -cos

tan(180- )       =   MP/-OM  =  -tan

cot(180- )       =  -OM/MP   =  -cot

sec(180- )       =   OP/-OM  =  -sec

cosec(180- )   =   OP/MP    =   cosec

Discussion of Exercises of SL Loney Plane Trigonometry Solutions Chapter 5: Trigonometric Functions

• In Chapter 5 of Loney Plane Trigonometry Solutions, you will come across with the various functions of trigonometry.
• You will be asked to prove a few statements and also find the values using various trigonometric ratios.
• As you will move forward, you will get the problems where you will be asked to express in terms of ratios for various angles.
• The exercise of chapter 5 Trigonometric Functions does not only involve comprehensive questions but at the same time, you will witness both basic and standard questions related to the different functions explained in the chapter.

Why Use SL Loney Plane Trigonometry Solutions Chapter 5: Trigonometric Functions by Instasolv?

1. Instasolv focuses to aid you to solve your doubts and help you prepare confidently for your exams. Our subject matter experts have provided easy step by step solutions for SL Loney Solutions for all the problems in a clear way.
2. The method used in our solution is made without any complexity so that you do not face any issue while learning the chapter.
3. Understanding Trigonometry is not as easy as it sounds but with our solutions you will get rid of any scepticism you possess in mind.
4. With the combination of your consistent effort and our brilliant SL Loney solutions, you can get to the peak of learning.
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