CBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 8 Introduction to Trigonometry. According to new CBSE Exam Pattern,Ā MCQ Questions for Class 10 Maths Carries 20 Marks. https://www.cbselabs.com/introduction-to-trigonometry-class-10-notes/
CBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry
- Position of a point P in the Cartesian plane with respect to co-ordinate axes is represented by the ordered pair (x, y).
- Trigonometry is the science of relationships between the sides and angles of a right-angled triangle.
- Trigonometric Ratios: Ratios of sides of right triangle are called trigonometric ratios.
Consider triangle ABC right-angled at B. These ratios are always defined with respect to acute angle ‘A’ or angle āC. - If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of an angle can be easily determined.
- How to identify sides: Identify the angle with respect to which the t-ratios have to be calculated. Sides are always labelled with respect to the ‘Īø’ being considered.
Trigonometry Class 10 Notes Chapter 8
Let us look at both cases:
In a right triangle ABC, right-angled at B. Once we have identified the sides, we can define six t-Ratios with respect to the sides.
case I | case II |
(i) sine A =Ā \(\frac { perpendicular }{ hypotenuse } =\frac { BC }{ AC } \) | (i) sine C =Ā \(\frac { perpendicular }{ hypotenuse } =\frac { AB }{ AC } \) |
(ii) cosine A =Ā \(\frac { base }{ hypotenuse } =\frac { AB }{ AC } \) | (ii) cosine C =Ā \(\frac { base }{ hypotenuse } =\frac { BC }{ AC } \) |
(iii) tangent A =Ā \(\frac { perpendicular }{ base } =\frac { BC }{ AB } \) | (iii) tangent C =Ā \(\frac { perpendicular }{ base } =\frac { AB }{ BC } \) |
(iv) cosecant A =Ā \(\frac { hypotenuse }{ perpendicular } =\frac { AC }{ BC } \) | (iv) cosecant C =Ā \(\frac { hypotenuse }{ perpendicular } =\frac { AC }{ AB } \) |
(v) secant A =Ā \(\frac { hypotenuse }{ base } =\frac { AC }{ AB } \) | (v) secant C =Ā \(\frac { hypotenuse }{ base } =\frac { AC }{ BC } \) |
(v) cotangent A =Ā \(\frac { base }{ perpendicular } =\frac { AB }{ BC } \) | (v) cotangent C =Ā \(\frac { base }{ perpendicular } =\frac { BC }{ AB } \) |
Note from above six relationships:
cosecant A = \(\frac { 1 }{ sinA }\), secant A = \(\frac { 1 }{ cosineA }\), cotangent A = \(\frac { 1 }{ tanA }\),
However, it is very tedious to write full forms of t-ratios, therefore the abbreviated notations are:
sine A is sin A
cosine A is cos A
tangent A is tan A
cosecant A is cosec A
secant A is sec A
cotangent A is cot A
Introduction To Trigonometry Class 10 Notes Chapter 8
TRIGONOMETRIC IDENTITIES
An equation involving trigonometric ratio of angle(s) is called a trigonometric identity, if it is true for all values of the angles involved. These are:
tan Īø = \(\frac { sin\theta }{ cos\theta } \)
cot Īø = \(\frac { cos\theta }{ sin\theta } \)
- sinĀ² Īø + cosĀ² Īø = 1 ā sinĀ² Īø = 1 – cosĀ² Īø ā cosĀ² Īø = 1 – sinĀ² Īø
- cosecĀ² Īø – cotĀ² Īø = 1 ā cosecĀ² Īø = 1 + cotĀ² Īø ā cotĀ² Īø = cosecĀ² Īø – 1
- secĀ² Īø – tanĀ² Īø = 1 ā secĀ² Īø = 1 + tanĀ² Īø ā tanĀ² Īø = secĀ² Īø – 1
- sin Īø cosec Īø = 1 ā cos Īø sec Īø = 1 ā tan Īø cot Īø = 1
ALERT:
A t-ratio only depends upon the angle āĪøā and stays the same for same angle of different sized right triangles.
Trigonometry Notes Class 10 Chapter 8
Value of t-ratios of specified angles:
ā A | 0Ā° | 30Ā° | 45Ā° | 60Ā° | 90Ā° |
sin A | 0 | \(\frac { 1 }{ 2 }\) | \(\frac { 1 }{ \sqrt { 2 } } \) | \(\frac { \sqrt { 3 } }{ 2 } \) | 1 |
cos A | 1 | \(\frac { \sqrt { 3 } }{ 2 } \) | \(\frac { 1 }{ \sqrt { 2 } } \) | \(\frac { 1 }{ 2 }\) | 0 |
tan A | 0 | \(\frac { 1 }{ \sqrt { 3 } } \) | 1 | ā3 | not defined |
cosec A | not defined | 2 | ā2 | \(\frac { 2 }{ \sqrt { 3 } } \) | 1 |
sec A | 1 | \(\frac { 2 }{ \sqrt { 3 } } \) | ā2 | 2 | not defined |
cot A | not defined | ā3 | 1 | \(\frac { 1 }{ \sqrt { 3 } } \) | 0 |
The value of sin Īø and cos Īø can never exceed 1 (one) as opposite side is 1. Adjacent side can never be greater than hypotenuse since hypotenuse is the longest side in a right-angled ā.
Introduction Of Trigonometry Class 10 Chapter 8
‘t-RATIOS’ OF COMPLEMENTARY ANGLES
If āABC is a right-angled triangle, right-angled at B, then
ā A + ā C = 90Ā° [āµ ā A + ā B + ā C = 180Ā° angle-sum-property]
or ā C = (90Ā° – ā A)
Thus, ā A and ā C are known as complementary angles and are related by the following relationships:
sin (90Ā° -A) = cos A; cosec (90Ā° – A) = sec A
cos (90Ā° – A) = sin A; sec (90Ā° – A) = cosec A
tan (90Ā° – A) = cot A; cot (90Ā° – A) = tan A
Class 10 Trigonometry Notes Chapter 8
Class 10 Maths Notes
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- Chapter 4 Quadratic Equations Class 10 Notes
- Chapter 5 Arithmetic Progressions Class 10 Notes
- Chapter 6 Triangles Class 10 Notes
- Chapter 7 Coordinate Geometry Class 10 Notes
- Chapter 8 Introduction to Trigonometry Class 10 Notes
- Chapter 9 Some Applications ofĀ Trigonometry Class 10 Notes
- Chapter 10 Circles Class 10 Notes
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