The eighth chapter in Mathematics textbook is '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 ‘C. - 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 ‘θ’ being considered.
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
The topics discussed in this chapter are as follows:
- Trigonometric Ratios
- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
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NCERT Solutions for Chapter 8: Introduction to Trigonometry
Also Check
Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progression
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 9: Some Applications of Trigonometry
Chapter 10: Circle
Chapter 11: Constructions
Chapter 12: Areas Related to Circles
Chapter 13: Surface Areas and Volume
Chapter 14: Statistics
Chapter 15: Probability
Check out Frequently Asked Questions (FAQs) for Chapter 8: Introduction to Trigonometry
(Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to
sin 30° = ½, sin 60° = √3/2, cos 30° = √3/2 and cos 60° = ½
Putting these values, we get:
(½+½)-(√3/2+√3/2)
= 1 – [(2√3)/2]
= 1 – √3
sin (90° – A) and cos A are
By trigonometry identities.
Sin (90°-A) = cos A {since 90°-A comes in the first quadrant of unit circle}
Hence, both are same.
If cos X = a/b, then sin X is equal to
cos X = a/b
By trigonometry identities, we know that:
sin2X + cos2X = 1
sin2X = 1 – cos2X = 1-(a/b)2
sin X = √(b2-a2)/b
sin 2A = 2 sin A is true when A =
sin 2A = sin 0° = 0
2 sin A = 2 sin 0° = 0
If ∆ABC is right angled at C, then the value of cos(A+B) is
Given that in a right triangle ABC, ∠C = 90°.
We know that the sum of the three angles is equal to 180°.
∠A + ∠B + ∠C = 180°
∠A + ∠B + 90° = 180° (∵ ∠C = 90° )
∠A + ∠B = 90°
Now, cos(A+B) = cos 90° = 0