Trigonometric equations class 11

NCERT Solutions of Chapter 3 Class 11 Trigonometry is available free at teachoo. You can check the detailed explanation of all questions of exercises, examples and miscellaneous by clicking on the Exercise link below. We had learned Basics of Trigonometry in Class 10. In this chapter, we will learn • What is a positive or a negative angle • Measuring angles in Degree, Minutes and Seconds • Radian measure of an angle • Converting Degree to Radians, and vice-versa • Sign of sin, cos, tan in all 4 quadrants • Finding values of trigonometric functions when one value is given (Example: Finding value of sin, cot, cosec, tan, sec, when cos x = -3/5 is given) • Finding Value of trigonometric functions, given angle • Solving questions by formula like (x + y) formula, 2x 3x formula, Cos x + cos y formula , 2 sin x sin y formula • Finding principal and general solutions of a trigonometric equation • Sin and Cosine Formula with supplementary Questions Important questions are marked, and Formula sheet is also provided. Click on an exercise or topic to begin.

1. Soln: Trigonometric equation: An equation involving trigonometric function or function of variable is called trigonometric equation. e.g. (i) sinx = $\frac$ , n ԑ Z.

Reciprocal Identities: $cosec(x) = \frac $ |cos x|=1, general solution is given by $x=n \pi$ Some basics Tips to solve the trigonometry questions (1) Always try to bring the multiple angles to single angles using the basic formula. Make sure all your angles are the same. Using $sin(2x)$ and $sin(x)$ is difficult, but if you use $sin(2x) = 2 sin(x)cos(x)$, that leaves $sin(x)$ and $cos(x)$, and now all your functions match. The same goes for addition and subtraction: don’t try working with $sin(x+y)$ and $sin (x-y)$. Instead, use $sin(X+Y) = sin(x)cos(y)+cos(x)sin(y)$ so that all the angles match (2) Converting to sin and cos all the items in the problem using a basic formula. I have mentioned sin and cos as they are easy to solve. You can use any other also. (3)Check all the angles for sums and differences and use the appropriate identities to remove them. (4) Use Pythagorean identifies to simplify the equations (5) Practice and Practice. You will soon start figuring out the equation and their symmetry to resolve them fast Download all the trigonometry Formulas below Hope you like this compilation of Trigonometry Formulas for class 11. This will be very useful for the Maths students Download Trigonometry Formulas PDF

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-4. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-4(a), Exe-4(b), Exe-4(c), Exe-4(d) with Chapter Test Questions. Visit official Website Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Class: 11th Subject: Mathematics Chapter : Ch-4 Trigonometrical Functions of Section -A Chapter Test Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Angle Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative. Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°. Relation Between Radian and Degree We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°. 2π radian = 360°. Hence, π radian = 180° or 1 radian = 57° 16′ 21″ (approx) 1 degree = 0.01746 radian Trigonometric Equations Equation which involves trigonometric functions of unknown angles is known as the trigonometric equation. Solution of a Trigonometric Equation A ...

Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-6. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-6 with Chapter Test Questions. Visit official Website Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Class: 11th Subject: Mathematics Chapter : Ch-6 Trigonometric Equations Angles of Section -A Exe-6 Chapter Test Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Angle Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative. Measuring Angles There are two systems of measuring angles Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is ( 1 360 ) 𝑡 ℎ of a revolution, the angle is said to have a measure of one degree, written as 1°. One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written as 1″ Thus, 1° = 60′ and 1′ = 60″ Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°. Relation Between Radia...

Reciprocal Identities: $cosec(x) = \frac $ |cos x|=1, general solution is given by $x=n \pi$ Some basics Tips to solve the trigonometry questions (1) Always try to bring the multiple angles to single angles using the basic formula. Make sure all your angles are the same. Using $sin(2x)$ and $sin(x)$ is difficult, but if you use $sin(2x) = 2 sin(x)cos(x)$, that leaves $sin(x)$ and $cos(x)$, and now all your functions match. The same goes for addition and subtraction: don’t try working with $sin(x+y)$ and $sin (x-y)$. Instead, use $sin(X+Y) = sin(x)cos(y)+cos(x)sin(y)$ so that all the angles match (2) Converting to sin and cos all the items in the problem using a basic formula. I have mentioned sin and cos as they are easy to solve. You can use any other also. (3)Check all the angles for sums and differences and use the appropriate identities to remove them. (4) Use Pythagorean identifies to simplify the equations (5) Practice and Practice. You will soon start figuring out the equation and their symmetry to resolve them fast Download all the trigonometry Formulas below Hope you like this compilation of Trigonometry Formulas for class 11. This will be very useful for the Maths students Download Trigonometry Formulas PDF

1. Soln: Trigonometric equation: An equation involving trigonometric function or function of variable is called trigonometric equation. e.g. (i) sinx = $\frac$ , n ԑ Z.

NCERT Solutions of Chapter 3 Class 11 Trigonometry is available free at teachoo. You can check the detailed explanation of all questions of exercises, examples and miscellaneous by clicking on the Exercise link below. We had learned Basics of Trigonometry in Class 10. In this chapter, we will learn • What is a positive or a negative angle • Measuring angles in Degree, Minutes and Seconds • Radian measure of an angle • Converting Degree to Radians, and vice-versa • Sign of sin, cos, tan in all 4 quadrants • Finding values of trigonometric functions when one value is given (Example: Finding value of sin, cot, cosec, tan, sec, when cos x = -3/5 is given) • Finding Value of trigonometric functions, given angle • Solving questions by formula like (x + y) formula, 2x 3x formula, Cos x + cos y formula , 2 sin x sin y formula • Finding principal and general solutions of a trigonometric equation • Sin and Cosine Formula with supplementary Questions Important questions are marked, and Formula sheet is also provided. Click on an exercise or topic to begin.

Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-6. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-6 with Chapter Test Questions. Visit official Website Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Class: 11th Subject: Mathematics Chapter : Ch-6 Trigonometric Equations Angles of Section -A Exe-6 Chapter Test Trigonometric Equations Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Angle Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative. Measuring Angles There are two systems of measuring angles Sexagesimal system (degree measure): If a rotation from the initial side to terminal side is ( 1 360 ) 𝑡 ℎ of a revolution, the angle is said to have a measure of one degree, written as 1°. One sixtieth of a degree is called a minute, written as 1′ and one-sixtieth of a minute is called a second, written as 1″ Thus, 1° = 60′ and 1′ = 60″ Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°. Relation Between Radia...

Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-4. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-4(a), Exe-4(b), Exe-4(c), Exe-4(d) with Chapter Test Questions. Visit official Website Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Class: 11th Subject: Mathematics Chapter : Ch-4 Trigonometrical Functions of Section -A Chapter Test Trigonometrical Functions OP Malhotra S.Chand ISC Class-11 Maths Solutions Angle Angle is a measure of rotation of a given ray about its initial point. The original ray is called the initial side and the final position of ray after rotation is called terminal side of the angle. The point of rotation is called vertex. If the direction of rotation is anti-clockwise, the angle is said to be positive and if the direction of rotation is clockwise, then the angle is negative. Circular system (radian measure): A radian is an angle subtended at the centre of a circle by an arc, whose length is equal to the radius of the circle. We denote 1 radian by 1°. Relation Between Radian and Degree We know that a complete circle subtends at its centre an angle whose measure is 2π radians as well as 360°. 2π radian = 360°. Hence, π radian = 180° or 1 radian = 57° 16′ 21″ (approx) 1 degree = 0.01746 radian Trigonometric Equations Equation which involves trigonometric functions of unknown angles is known as the trigonometric equation. Solution of a Trigonometric Equation A ...