Trigonometry (Copy)
TRIGONOMETRY — O LEVEL & IGCSE ADDITIONAL MATHEMATICS FORMULA SHEET + COMMON MISTAKES
| Topic | Formula / Rule | Common Mistake |
|---|---|---|
| Sine Ratio | sinθ = opposite/hypotenuse | Mixing sides |
| Cosine Ratio | cosθ = adjacent/hypotenuse | Wrong denominator |
| Tangent Ratio | tanθ = opposite/adjacent | Using hypotenuse |
| Pythagoras Theorem | a² + b² = c² | Forgetting hypotenuse |
| Trig Identity | tanθ = sinθ/cosθ | Writing cos/sin |
| Exact Value | sin30° = 1/2 | Memorising wrongly |
| Exact Value | cos60° = 1/2 | Mixing with sin60° |
| Exact Value | tan45° = 1 | Wrong surd value |
| Exact Value | sin45° = √2/2 | Writing √2 |
| Exact Value | cos45° = √2/2 | Forgetting denominator |
| Exact Value | tan60° = √3 | Using 1/√3 |
| Exact Value | tan30° = 1/√3 | Using √3 |
| Quadrant Signs | ASTC rule | Wrong sign in quadrant |
| Sine Rule | a/sinA = b/sinB = c/sinC | Matching wrong side-angle pair |
| Cosine Rule | a² = b² + c² − 2bc cosA | Wrong sign before cosine |
| Area Formula | A = 1/2 ab sinC | Forgetting 1/2 |
| Small Angle Approximation | sinθ ≈ θ | Using degrees instead of radians |
| Radian Measure | π radians = 180° | Mixing units |
| Degree to Radian | × π/180 | Multiplying wrong way |
| Radian to Degree | × 180/π | Dividing incorrectly |
| Unit Circle | Radius = 1 | Using normal circle rules |
| Trig Graph | y = sinx | Wrong shape |
| Sine Graph Period | 2π | Writing π |
| Cosine Graph Period | 2π | Mixing with tangent |
| Tangent Graph Period | π | Writing 2π |
| Sine Graph Range | −1 ≤ y ≤ 1 | Wrong range |
| Cosine Graph Range | −1 ≤ y ≤ 1 | Wrong range |
| Tangent Graph Range | All real numbers | Saying restricted |
| Trig Equation | Solve within interval | Giving incomplete answers |
| Principal Values | Use inverse trig carefully | Wrong quadrant |
| Inverse Sine | sin⁻¹x | Confusing with reciprocal |
| Inverse Cosine | cos⁻¹x | Confusing notation |
| Inverse Tangent | tan⁻¹x | Using 1/tanx |
| Double Angle | sin2A = 2sinA cosA | Forgetting factor 2 |
| Double Angle | cos2A = cos²A − sin²A | Wrong sign |
| Double Angle | cos2A = 2cos²A − 1 | Missing −1 |
| Double Angle | cos2A = 1 − 2sin²A | Wrong coefficient |
| Trig Identity | sin²A + cos²A = 1 | Forgetting square |
| Secant | secθ = 1/cosθ | Using reciprocal wrongly |
| Cosecant | cosecθ = 1/sinθ | Mixing with sec |
| Cotangent | cotθ = 1/tanθ | Writing tanθ |
| Ambiguous Case | SSA can give 2 triangles | Giving one answer only |
| Bearing Questions | Measure clockwise from north | Measuring anticlockwise |
| Elevation Angle | Measured upward from horizontal | Using vertical |
| Depression Angle | Measured downward from horizontal | Wrong reference line |
| Calculator Mode | Use DEG or RAD correctly | Wrong mode |
| Graph Transformations | y = asin(bx + c) + d | Wrong shift direction |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
QUICK TRIG RATIOS TABLE
| Ratio | Formula |
|---|---|
| sinθ | opposite/hypotenuse |
| cosθ | adjacent/hypotenuse |
| tanθ | opposite/adjacent |
QUICK EXACT VALUES TABLE
| Angle | sinθ | cosθ | tanθ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | Undefined |
QUICK TRIG IDENTITIES TABLE
| Identity | Formula |
|---|---|
| Basic Identity | sin²A + cos²A = 1 |
| Tangent Identity | tanA = sinA/cosA |
| Reciprocal Identity | secA = 1/cosA |
| Reciprocal Identity | cosecA = 1/sinA |
| Reciprocal Identity | cotA = 1/tanA |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
QUICK RULES TABLE
| Rule | Formula |
|---|---|
| Sine Rule | a/sinA = b/sinB = c/sinC |
| Cosine Rule | a² = b² + c² − 2bc cosA |
| Triangle Area | A = 1/2 ab sinC |
| Pythagoras | a² + b² = c² |
QUICK GRAPH FEATURES TABLE
| Graph | Period | Range |
|---|---|---|
| y = sinx | 2π | −1 to 1 |
| y = cosx | 2π | −1 to 1 |
| y = tanx | π | All real numbers |
QUICK QUADRANT SIGNS TABLE
| Quadrant | Positive Function |
|---|---|
| 1st | All |
| 2nd | Sine |
| 3rd | Tangent |
| 4th | Cosine |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.
EXAM HACKS
| Situation | Fast Trick |
|---|---|
| Right triangle | SOHCAHTOA |
| Non-right triangle | Sine/Cosine Rule |
| Missing side with angle | Cosine Rule |
| Missing angle with sides | Sine Rule |
| Graph question | Check period and amplitude |
| Inverse trig | Think about quadrant |
| Bearings | Start from north clockwise |
| Calculator issue | Check DEG/RAD mode |
| Exact values | Memorise special angles |
| Trig identities | Convert everything to sin/cos |
MOST COMMON LOSSES OF MARKS
| Mistake | Why Marks Are Lost |
|---|---|
| Wrong trig ratio | Entire solution incorrect |
| Calculator in wrong mode | Wrong values |
| Mixing degrees and radians | Formula errors |
| Wrong sine/cosine rule pair | Incorrect answer |
| Sign mistakes in quadrants | Wrong angle |
| Forgetting ambiguous case | Missing solution |
| Incorrect graph shape | Sketch marks lost |
| Wrong exact values | Accuracy lost |
| Forgetting square in identity | Identity incorrect |
| Bearing measured wrong way | Entire geometry incorrect |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 11 World Records and 7 Distinctions, Educate A Change.