This circle has the centre at the origin and a radius of 1 unit. The point P can move around the circumference of the circle. At point P the \(x\)-coordinate is \(\cos{\theta}\) and the \(y ...

Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose equation in polar coordinates is \(r=1-2\cos\theta\text{,}\) \(0\leq \theta ...

An object is moving counter-clockwise along a circle with the centre at the origin. At \(t=0\) the object is at point \(A(0,5)\) and at \(t=2\pi\) it is back to point \(A\) for the first time.

2. Determine the roots of the equation \(\sqrt 5 \sin x + 2\cos x = 0\) in the interval \(0 \le x \le 2\pi\) 3. Sketch the graph of \(y = \sqrt 5 \sin x + 2\cos x\) for \(0 \le x \le 2\pi\) 4.