10
CBSE Marks
★★★★★
Difficulty
9
Topics
Very High
Board Weight
Topics Covered
9 key topics in this chapter
Trigonometric Ratios of Acute Angle
sin, cos, tan, cosec, sec, cot
Ratios of Specific Angles: 0°,30°,45°,60°,90°
Trigonometric Table
Trigonometric Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Complementary Angles
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Pythagorean Identity 1 | \(sin²θ + cos²θ = 1\) |
| Pythagorean Identity 2 | \(1 + tan²θ = sec²θ\) |
| Pythagorean Identity 3 | \(1 + cot²θ = cosec²θ\) |
| sin 30° / cos 60° | \(1/2\) |
| sin 45° / cos 45° | \(1/√2\) |
| sin 60° / cos 30° | \(√3/2\) |
| tan 45° | \(1\) |
| tan 30° | \(1/√3\) |
| tan 60° | \(√3\) |
Important Points to Remember
Trigonometric ratios are defined for acute angles in a right-angled triangle.
sin θ = Opp/Hyp; cos θ = Adj/Hyp; tan θ = Opp/Adj; cosec = 1/sin; sec = 1/cos; cot = 1/tan.
Complementary angles: sin(90°−θ) = cos θ, cos(90°−θ) = sin θ, tan(90°−θ) = cot θ.
Key identity: sin²θ + cos²θ = 1 is the mother of all trig identities at Class X level.