As a tangent is a straight line it is described by an equation in the form \(y - b = m(x - a)\). You need both a point and the gradient to find its equation. You are usually given the point - it's ...

A tangent to a circle at point P is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is ...

Transformations of Functions 1.3 An applet illustrating how transformations affect the graph of a function. Transformations are represented both algebraically and graphically. Construction of the ...

Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...