Trigonometry Class 10 Maths — Revision Notes
This chapter covers trigonometric ratios in right triangles and their applications. Students learn six main ratios, values at special angles, and trigonome
TL;DR: This chapter covers trigonometric ratios in right triangles and their applications. Students learn six main ratios, values at special angles, and trig…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
This chapter covers trigonometric ratios in right triangles and their applications. Students learn six main ratios, values at special angles, and trigonome
Trigonometric Ratios
- In right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
- cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
- Ratios depend on angle, not size of triangle
- ASTC rule: All positive in first quadrant, Sin in second, Tan in third, Cos in fourth
Trigonometric Values
- 0°: sin 0, cos 1, tan 0
- 30°: sin 1/2, cos sqrt(3)/2, tan 1/sqrt(3)
- 45°: sin 1/sqrt(2), cos 1/sqrt(2), tan 1
- 60°: sin sqrt(3)/2, cos 1/2, tan sqrt(3)
- 90°: sin 1, cos 0, tan undefined
Trigonometric Identities
- sin^2 θ + cos^2 θ = 1
- 1 + tan^2 θ = sec^2 θ
- 1 + cot^2 θ = cosec^2 θ
- sin θ / cos θ = tan θ
- sin(90 - θ) = cos θ, cos(90 - θ) = sin θ (complementary angles)
Applications
- Height and distance problems: angles of elevation and depression
- Angle of elevation: angle above horizontal when looking up
- Angle of depression: angle below horizontal when looking down
- Use trigonometric ratios to find unknown heights or distances
Key Terms
- Trigonometric Ratio: Ratio of sides in right triangle with respect to an angle
- Angle of Elevation: Angle above horizontal from observer to object above
- Angle of Depression: Angle below horizontal from observer to object below
Frequently Asked Questions
How do you find height of a building using trigonometry?
If angle of elevation is θ and distance from base is d, then height h = d tan(θ).
Why is sin^2 θ + cos^2 θ = 1?
From Pythagoras theorem in right triangle: (opposite)^2 + (adjacent)^2 = (hypotenuse)^2. Dividing by hypotenuse^2 gives sin^2 θ + cos^2 θ = 1.
More Class 10 Maths Revision Notes
- Real Numbers
- Polynomials
- Pair of Linear Equations in Two Variables
- Quadratic Equations
- Arithmetic Progressions
- Triangles
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →