Trigonometry is essential for O Level For the best math tuition Singapore, explore our structured programs designed for exam success. Math. This guide covers all the trigonometry you need to know.
Basic Trigonometric Ratios
In a right-angled triangle:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Remember: SOH CAH TOA
Special Angles
Memorise these values:
| θ | sin θ | cos θ | tan θ |
|—|——-|——-|——-|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
Pythagoras Theorem
In a right-angled triangle:
a² + b² = c²
Where c is the hypotenuse.
Use this to find unknown sides.
Trigonometric Identities
- sin²θ + cos²θ = 1
2. tan θ = sin θ / cos θ
3. 1 + tan²θ = sec²θ (less common)
These identities are useful for proving and simplifying.
Finding Unknown Sides
Given an angle and one side:
- Identify the relationship (sin, cos, or tan)
- 2. Write the equation
- 3. Solve for the unknown
Example: Find x in a right-angled triangle where the angle is 30° and the hypotenuse is 10.
cos 30° = x / 10
x = 10 × cos 30°
x = 10 × √3/2 = 5√3
Finding Unknown Angles
Given two sides:
- Identify the relationship
- 2. Calculate the ratio
- 3. Use inverse function (sin⁻¹, cos⁻¹, tan⁻¹)
Example: Find θ where opposite = 5, hypotenuse = 10.
sin θ = 5/10 = 0.5
θ = sin⁻¹(0.5) = 30°
Bearings
Bearings are angles measured clockwise from North.
Key Points:
- Always three digits (045°, not 45°)
- – Measured from North
- – Clockwise direction
Example: A bearing of 090° is East.
A bearing of 180° is South.
3D Trigonometry
For 3D problems:
- Draw or visualise the relevant triangles
- 2. Apply 2D trigonometry to each triangle
- 3. Connect the results
Common types:
- Angle between line and plane
- – Angle between two planes
Sine Rule
For any triangle:
a / sin A = b / sin B = c / sin C
Use when:
- Given two angles and one side
- – Given two sides and a non-included angle
Cosine Rule
For any triangle:
a² = b² + c² – 2bc cos A
Or rearranged:
cos A = (b² + c² – a²) / 2bc
Use when:
- Given three sides
- – Given two sides and the included angle
Area of a Triangle
Area = (1/2)ab sin C
Works for any triangle when you know two sides and the included angle.
Common Mistakes
Wrong Ratio:
Using sin when you should use cos or tan.
Degree Mode:
Calculator in radians instead of degrees.
Ambiguous Case:
Sine rule can give two possible angles.
Units:
Mixing degrees and radians.
Practice Tips
Memorise Special Angles:
They come up frequently.
Draw Diagrams:
Always sketch the triangle.
Label Everything:
Mark angles and sides clearly.
Check Reasonableness:
Should the angle be acute or obtuse?
How Ace Scorers Helps
Our Math programme covers trigonometry thoroughly:
- Clear concept explanations
- – Plenty of practice
- – Exam-focused preparation
- – Application problems
Contact us for Math tuition.
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