WAEC SSCE Further Mathematics
Study notes for Co-ordinate Geometry — part of the WAEC SSCE Further Mathematics syllabus. 3 learning objectives with explanations and exam tips.
When you're dealing with angles in coordinate geometry, compound angles involve adding or subtracting two angles together. Think of it like combining two rotations—if you rotate a point by angle A, then by angle B, you've used a compound angle A + B. Multiple angles are when you multiply an angle by a number, like 2A or 3A.
For example, imagine navigating from Lagos to Ibadan using two different direction changes. Your first turn involves angle A and your second involves angle B. To find your overall direction, you calculate the compound angle A + B using formulas like sin(A + B) = sinA cosB + cosA sinB.
These formulas help you find exact coordinates of rotated points without measuring manually. They're essential for solving problems about reflecting or rotating geometric shapes on a coordinate plane.
Trigonometric functions help us describe how points move around circles and waves in coordinate planes. When you plot angles in standard position (starting from the positive x-axis), sine gives you the vertical distance, cosine gives the horizontal distance, and tangent is their ratio. Think of it like tracking a footballer's position on a circular running track at Lagos National Stadium—the angle tells you where he is, and sine/cosine tell you his exact coordinates.
Solving trigonometric equations means finding all angles that satisfy a given condition. For example, if sin(θ) = 0.5, you need to find every angle where this is true, remembering that solutions repeat every 360°. The key is understanding that one trigonometric value corresponds to multiple angles.
A straight line is the shortest distance between two points on a plane. In Further Mathematics, we represent straight lines using equations. The most common form is y = mx + c, where m is the slope (how steep the line is) and c is the y-intercept (where the line crosses the y-axis).
Think of it like a road connecting Lagos to Ibadan. The slope tells you how quickly the road climbs or descends, while the y-intercept shows where your journey starts on a vertical axis.
You can find a line's equation if you know two points or one point and the slope. The gradient formula is m = (y₂ - y₁)/(x₂ - x₁). Two lines are parallel when they have equal slopes, and perpendicular when their slopes multiply to give -1.