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# Trigonometry-CBSE CLASS 11

Trigonometry-CBSE CLASS 11

CONTENT LIST

## Trigonometry

The branch of mathematics that deals the properties of trigonometric functions and their application to the determination of the angles and sides of triangles.

### Angle

When a ray AB starting from its initial position and rotates about its end point A and takes the final position AC, we say that an angle BAC (written as ∠ BAC) has been formed.

The amount of rotation from the initial side AB to the terminal side AC is termed as the measure of the angle.

### Positive and Negative Angles

Positive Angles

An angle formed by a rotating ray is said to be positive if rotation is anticlock wise.

Negative Angles

An angle formed by a rotating ray is said to be negative if rotation is clock wise.

### Measurement of Angles

There are three system for measuring angles,

• Sexagesimal System(Degree Measure)
• Centesimal System

Sexagesimal System(Degree Measure)

In Sexagesimal System, a right angle is divided into 90 equal parts,one part is known as degree. Symbol ° is used to expres degree.

One degree is divided into 60 equal parts, termed as minutes.Symbol ′ is used to expres minutes.

One minute is divided into 60 equal parts, termed as seconds. Symbols ″ are used to denote seconds.

Centesimal System

In Centesimal System, a right angle is divided into 90 equal parts, one part is known as grades.

One grades is divided into 100 equal parts, termed as minutes.Symbol ′ is used to expres minutes.

One minute is divided into 100 equal parts, termed as seconds. Symbols ″ are used to denote seconds.

In this system, angle is measured in term of radian.

A radian is the angle subtended at the centre of a circle by an arc of equal length of radius of the circle.

## Trigonometric Ratios

Trigonometric ratios or T-ratios express relation between different sides and angles of a right angled triangle.

There are six trigonometric ratios or T-ratios.These are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

sine: Sine of an angle is the ratio of perpendicular to the hypotenuse.

cosine: Cosine of an angle the ratio of the base to the hypotenuse.

tangent: Tangent of an angle is the ratio of perpendicular to the

cosecant: Cosecant is a multiplicative inverse of sine.

secant: Secant is a multiplicative inverse of cosine.

cotangent: Cotangent is the multiplicative inverse of the tangent.

The x-axis and y-axis of a two-dimensional Cartesian plane system divide the plane into four regions called quadrants.

## How to find value of trigometric function of any angle?

Step 1: Convert the given angle in term of (Nx90°+θ°)

Step 2: Case A: If N= even number than there will no change in trigonmetric function .

Case B: If N= odd number than there will change in trigonmetric function .

• sin will change to cos .
• cos will change to sin .
• tan will change to cot .
• sec will change to cosec .
• cosec will change to sec .
• cot will change to tan .

Step 3: Idenify the quadrent of given angle and give sign +/- accordingly .

Example:1

Example:2

Question: What would be the value of sin15°?
a) (√3 – 1) / √2
b)(√3 – 1) / 2√2
c)(√3 – 1) / 2
d) None of these

Solution

sin15°= sin(45° – 30°) = (sin45° . cos30°) – (cos45° . sin30°)
sin15° = (1/√2 . √3/2) – (1/√2 . ½)
sin15° = (√3 – 1) / 2√2
Question: Which of following is equal to cos²(28°)−sin²(28°)?
a) 1
b) cos56°
c) sin28°
d) None of these

Solution

We know that,
cos(2A) = cos²A - sin²A
putting A=28°
cos²(28°)−sin²(28°)= cos56°
Question: Which of following is equal to 6sin(5x)cos(5x)?
a) sin(10x)
b) 3sin²(10x)
c) 3sin(10x)
d) None of these

Solution

We know that,
sin(2A) =2sinA.cosA
putting A=5x
6sin(5x)cos(5x)= 3sin(10x)
Question: Which of following is equal to 1−2sin²(17°)?
a) sin(34°)
b) cos²(34°)
c) cos(34°)
d) None of these