# S.L. Loney Application of Algebraic Sign to Trigonometry Solutions (Chapter 4)

SL Loney Plane Trigonometry Solutions Chapter 4 ‘Application of Algebraic Signs to Trigonometry’ are created by subject matter experts of Instasolv to help you prepare for competitive tests like NEET and IIT JEE. All these solutions are as per the latest JEE syllabus. Application of Algebraic Signs to Trigonometry is an essential chapter of SL Loney Solutions to get an in-depth knowledge of how algebra and trigonometry can be combined. It clears your concept of how a revolving line can trace positive and negative angles, the idea of positive and negative direction with respect to a reference point. Formulas for Versed Sine and Coversed Sine of any angle is also discussed here.

SL Loney Plane Trigonometry Solutions for JEE** **Chapter 4 ‘Application of Algebraic Signs to Trigonometry’ has a total of 12 questions. You learn about different trigonometric ratios of different angles, Sine/Cosine/Tangent, and their reciprocal ratios. Also, you will find out how the sign of an angle changes based on the quadrant in which the revolving line lies. The tracing of the changes in the sign and magnitude of an angle’s trigonometric ratios (when the angle moves from 0 to 360 degrees) is dealt with detail in our solutions. They also explain how to represent the variation of this change of sign graphically.

Complete solutions to SL Loney Trigonometry for JEE and NEET** **have been meticulously provided by our team of mathematics experts, using which you can get in-depth knowledge of all the aspects of trigonometry. You will be able to better your computational skills and learn the concepts rather than just mugging up some formulas.

## Important Topics for SL Loney Plane Trigonometry Solutions Chapter 4: Application of Algebraic Signs to Trigonometry

**Positive and negative angles: **Angles are classified as positive or negative based on the quadrant in which they lie, in a co-ordinate axis. The 4 quadrants of Cartesian axes are depicted below:

When the line is rotated anti-clockwise, we get a positive angle and when it is rotated anti-clockwise it makes a negative angle.

As the line rotates, both x and y coordinates are positive in the 1^{st} quadrant, in the 2^{nd} quadrant x co-ordinate becomes negative, in the 3^{rd} quadrant both x and y are negative and in the 4^{th} quadrant x is positive and y is negative.

The angle made by the rotating line is always acute and is measured along the x-axis.

**Positive and negative lines – **For measuring distances, it is convenient to take one standard direction as positive and the direction opposite to it as negative. Normally, if we draw a line parallel to the foot of the page and O is a point on that line, then a point A on its side is said to be in a positive direction and a point A’ on the left of O is said to be in the negative direction.

If distances OA and OA’ both have a measurement of a, then the point is said to be at a distance of +a from O, and point A’ is at a distance of –a. If we draw a perpendicular line BB’ to the point O when B is towards the top of the page and B’ is towards the foot of the page, then all the lines going in the direction of OB have positive measurements and the lines in the direction of OB’ have negative measurements.

**Trigonometrical ratios of any angle – **In the above example if we draw a line OP, in either positive or negative direction, and draw a perpendicular from point P to the line AOA’ (let us say PM), then the different trigonometric ratios of angle AOP (let us say it is q) are given by:

Sine = MP/OP

Cosine = OM/OP

Tangent = MP/OM

Cotangent = OM/MP

Secant = OP/OM

Cosecant = OP/MP

T**rigonometrical Formulas – **For any angle q, following formulas hold true:

Sin^{2} + Cos^{2} = 1

Tan = Sin /Cos

Sec^{2} = I + tan^{2}

Cosec^{2} = 1 + cot^{2}

**Periods of Trigonometrical functions – **As the revolving line completes a full circle, encompassing all the quadrants and goes from 0 to 2π radians

- The sine of the angle changes from 0 to 1, then 1 to -1 and then from -1 to 0. The same changes happen when the angle goes from 2 π to 4 π. This is termed as a period of Sine is 2 π.
- Cosine, Secant, and Cosecant go through the same changes as Sine of an angle.
- Tangent and Cotangent go through these changes from 0 to π hence their period is π.

### Discussion of Exercises of SL Loney Plane Trigonometry Solutions Chapter 4: Application of Algebraic Signs to Trigonometry

- SL Loney Plane Trigonometry Application of Algebraic Signs to Trigonometry has only 1 exercise with 12 questions. The questions are based on trigonometric functions and ratios.
- You will be able to apply these functions and ratios to find degrees, minutes and seconds in a circle.
- There are questions based on the concept of centesimal and sexagesimal seconds and converting radians to seconds and vice versa.
- In some questions, you are given one trigonometrical ratio and you have to find the other ratios and express one formula of trigonometry in terms of a different ratio.

## Why Use SL Loney Plane Trigonometry Solutions Chapter 4: Application of Algebraic Signs to Trigonometry by Instasolv?

- Getting through any competitive exams like JEE and NEET requires rigorous practice as well as having sound knowledge of the topics, not just cramming formulas.
- With this in mind, we have provided SL Loney Trigonometry detailed solutions by breaking down any problem in small steps so that it clarifies your doubt at each step.
- Our solutions are free of cost so no monetary burden will come in the way of your exam preparations and future.
- We are here to help you by providing strategies and tips to combat the stressful exam environment by better managing your time.
- Our solutions are in adherence to the latest trigonometry syllabus for IIT JEE.