Instructions
What you can see
The main part of this applet is the big grey circle. There is a small red circle on the circumference which you can move to change the angle. The angle will be displayed as an orange sector as you might expect, behaviour of which is controlled by the green ranges switch (see below).
How to change the angle
There are 3 ways to do this.
- Click and drag: Move the small circle, it will stay 'attached' to the nearest point on the circumference.
- Keyboard arrows: You may have to click on the applet for your internet browser to focus on it, but then each press of an arrow key will increase or decrease the angle by \(1^{\circ}\) accordingly.
- Arrow buttons on screen: Click these to increase or decrease the angle by \(15^{\circ}\), as well as rounding the angle to the nearest \(15^{\circ}\).
This last method is better for learning key points and relations, especially as most of the radian measurements on these points are displayed in terms of \(\pi\).
Changing the range
The range by default is \(-\pi < \theta \leq \pi\). This is often the principal values range and is convention in graphs. However,
if you'd rather use the range \(0\leq\theta<2\pi\) then simply click the green button to change between them.
It can be interesting to choose an angle and then change back and forth between ranges to see the relationships between angles in a full circle!
The range affects whether the angle is taken clockwise or anticlockwise from the horizontal axis for angles in the lower half of the circle.
It would be best to become comfortable with both!
Glitches
If you find any issues, let me know on Twitter: @nextlevelmaths.