TRIGONOMETRY MASTER SHEET
High-Yield Formula Reference & Comprehensive Study Notes EXAM REVISION
1. RIGHT-ANGLED TRIANGLE RATIOS (SOH CAH TOA)
Defined for an acute angle θ in a right-angled triangle with Opposite (O), Adjacent (A), and Hypotenuse (H).
PRIMARY RATIOS RECIPROCAL RATIOS
Sine: sin(θ) = O / H Cosecant: csc(θ) = 1 / sin(θ) = H / O
Cosine: cos(θ) = A / H Secant: sec(θ) = 1 / cos(θ) = H / A
Tangent: tan(θ) = O / A = sin(θ) / cos(θ) Cotangent: cot(θ) = 1 / tan(θ) = A / O
2. EXACT SPECIAL VALUES TABLE
Degrees Radians sin(θ) cos(θ) tan(θ) csc(θ) sec(θ) cot(θ)
0° 0 0 1 0 Undefined 1 Undefined
30° π/6 1/2 √ 1 / √3 2 2 / √3 √3
45° π/4 1 / √2 1 / √2 1 √2 √2 1
60° π/3 √ 1/2 √3 2 / √3 2 1 / √3
90° π/2 1 0 Undefined 1 Undefined 0
180° π 0 -1 0 Undefined -1 Undefined
270° 3π / 2 -1 0 Undefined -1 Undefined 0
360° 2π 0 1 0 Undefined 1 Undefined
3. UNIT CIRCLE & ASTC QUADRANT SYSTEM
Coordinates on a unit circle are defined as (x, y) = (cos θ, sin θ). Use the "All Students Take Calculus" rule:
Quadrant II: 90° < θ < 180° (S) Quadrant I: 0° < θ < 90° (A)
• Sine & Csc positive (+) • ALL ratios positive (+)
• Cosine, Tan negative (−) • Primary active zone
θ = 180° − θ
• Reference: ref θ =θ
• Reference: ref
Quadrant III: 180° < θ < 270° (T) Quadrant IV: 270° < θ < 360° (C)
• Tangent & Cot positive (+) • Cosine & Sec positive (+)
• Sine, Cosine negative (−) • Sine, Tangent negative (−)
• Reference: θref = θ − 180° • Reference: θref = 360° − θ
Memorization Trick: All Students Take Calculus (QI: All, QII: Sin, QIII: Tan, QIV: Cos).
Trigonometry Quick Study Guide Page 1 of 2
High-Yield Formula Reference & Comprehensive Study Notes EXAM REVISION
1. RIGHT-ANGLED TRIANGLE RATIOS (SOH CAH TOA)
Defined for an acute angle θ in a right-angled triangle with Opposite (O), Adjacent (A), and Hypotenuse (H).
PRIMARY RATIOS RECIPROCAL RATIOS
Sine: sin(θ) = O / H Cosecant: csc(θ) = 1 / sin(θ) = H / O
Cosine: cos(θ) = A / H Secant: sec(θ) = 1 / cos(θ) = H / A
Tangent: tan(θ) = O / A = sin(θ) / cos(θ) Cotangent: cot(θ) = 1 / tan(θ) = A / O
2. EXACT SPECIAL VALUES TABLE
Degrees Radians sin(θ) cos(θ) tan(θ) csc(θ) sec(θ) cot(θ)
0° 0 0 1 0 Undefined 1 Undefined
30° π/6 1/2 √ 1 / √3 2 2 / √3 √3
45° π/4 1 / √2 1 / √2 1 √2 √2 1
60° π/3 √ 1/2 √3 2 / √3 2 1 / √3
90° π/2 1 0 Undefined 1 Undefined 0
180° π 0 -1 0 Undefined -1 Undefined
270° 3π / 2 -1 0 Undefined -1 Undefined 0
360° 2π 0 1 0 Undefined 1 Undefined
3. UNIT CIRCLE & ASTC QUADRANT SYSTEM
Coordinates on a unit circle are defined as (x, y) = (cos θ, sin θ). Use the "All Students Take Calculus" rule:
Quadrant II: 90° < θ < 180° (S) Quadrant I: 0° < θ < 90° (A)
• Sine & Csc positive (+) • ALL ratios positive (+)
• Cosine, Tan negative (−) • Primary active zone
θ = 180° − θ
• Reference: ref θ =θ
• Reference: ref
Quadrant III: 180° < θ < 270° (T) Quadrant IV: 270° < θ < 360° (C)
• Tangent & Cot positive (+) • Cosine & Sec positive (+)
• Sine, Cosine negative (−) • Sine, Tangent negative (−)
• Reference: θref = θ − 180° • Reference: θref = 360° − θ
Memorization Trick: All Students Take Calculus (QI: All, QII: Sin, QIII: Tan, QIV: Cos).
Trigonometry Quick Study Guide Page 1 of 2
