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 ...

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 a ...

As the tangent is a straight line, the equation of the tangent will be of the form \(y = mx + c\). We can use perpendicular gradients to find the value of \(m\), then use the coordinates of P to find ...