Trigonometry – MOST IMPORTANT NOTES (Class 10
Board)
1. Trigonometric Ratios
sin θ = Opp/Hyp, cos θ = Adj/Hyp, tan θ = Opp/Adj
cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
SOH–CAH–TOA
2. Fundamental Trigonometric Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
3. Standard Trigonometric Values
θ 0° 30° 45° 60° 90°
sin θ 0 1/2 1/√2 √3/2 1
cos θ 1 √3/2 1/√2 1/2 0
tan θ 0 1/√3 1 √3 ND
cosec θ ND 2 √2 2/√3 1
sec θ 1 2/√3 √2 2 ND
cot θ ND √3 1 1/√3 0
4. Complementary Angle Identities
sin(90° − θ) = cos θ
cos(90° − θ) = sin θ
tan(90° − θ) = cot θ
sec(90° − θ) = cosec θ
cosec(90° − θ) = sec θ
cot(90° − θ) = tan θ
5. Heights & Distances – Key Points
Angle of Elevation: Object above eye level
Angle of Depression: Object below eye level
Always draw diagram first.
6. Board Exam Tips
• Start identity proofs from LHS only
• Do not write tan 90° = ∞, write Not Defined
• Steps carry marks, do not skip steps
Board)
1. Trigonometric Ratios
sin θ = Opp/Hyp, cos θ = Adj/Hyp, tan θ = Opp/Adj
cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
SOH–CAH–TOA
2. Fundamental Trigonometric Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
3. Standard Trigonometric Values
θ 0° 30° 45° 60° 90°
sin θ 0 1/2 1/√2 √3/2 1
cos θ 1 √3/2 1/√2 1/2 0
tan θ 0 1/√3 1 √3 ND
cosec θ ND 2 √2 2/√3 1
sec θ 1 2/√3 √2 2 ND
cot θ ND √3 1 1/√3 0
4. Complementary Angle Identities
sin(90° − θ) = cos θ
cos(90° − θ) = sin θ
tan(90° − θ) = cot θ
sec(90° − θ) = cosec θ
cosec(90° − θ) = sec θ
cot(90° − θ) = tan θ
5. Heights & Distances – Key Points
Angle of Elevation: Object above eye level
Angle of Depression: Object below eye level
Always draw diagram first.
6. Board Exam Tips
• Start identity proofs from LHS only
• Do not write tan 90° = ∞, write Not Defined
• Steps carry marks, do not skip steps
