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 ...

\((x^2+y^2)^3=(y^2-x^2)\text{.}\) Multiply by \(r^2\) and use the fact that \(\cos 2\theta =cos ^2\theta -\sin ^2\theta\) See Figure 6.15.1. Figure 6.15.1. \(r=1+\sin ...

In the study of circular functions, the unit circle plays a central role in linking angles with trigonometric values. By defining sine, cosine, and tangent in terms of coordinates on a circle of ...

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 ...

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 ...