Summary
Trigonometry involves the study of angles and the relationships between the sides of triangles. It includes understanding trigonometric ratios, angles in different quadrants, and the properties of trigonometric functions.
- Trigonometric Ratios — Ratios of the sides of a right triangle relative to an angle. Example: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.
- Angle Measurement — An angle is measured from the positive x-axis, with anticlockwise as positive and clockwise as negative. Example: θ in the second quadrant is an obtuse angle.
- Trigonometric Functions — Functions like sine, cosine, and tangent that are periodic and have specific properties. Example: y = sin(θ) has a period of 2π and amplitude of 1.
- Reciprocal Ratios — Ratios like cosecant, secant, and cotangent that are reciprocals of sine, cosine, and tangent. Example: cosec(θ) = 1/sin(θ).
- Compound and Double Angle Formulae — Formulas that express trigonometric functions of sums or differences of angles. Example: sin(A + B) = sin(A)cos(B) + cos(A)sin(B).
Exam Tips
Key Definitions to Remember
- Trigonometric Ratios: sin, cos, tan
- Reciprocal Ratios: cosec, sec, cot
- Period and Amplitude of Trigonometric Functions
Common Confusions
- Mixing up the signs of trigonometric functions in different quadrants
- Confusing the period of sine and cosine with that of tangent
Typical Exam Questions
- What is the value of sin(45°)? Answer: √2/2
- How do you express sin(x) + √3 cos(x) in the form R sin(x + α)? Answer: Use the identity R sin(x + α) = a sin(x) + b cos(x)
- What is the period of y = tan(θ)? Answer: π
What Examiners Usually Test
- Understanding and application of trigonometric identities
- Ability to solve trigonometric equations
- Graph transformations of trigonometric functions