Trig 1 - Stuff About Circles

 

Radians

A Radian is a measure such that a segment with angle 1 Radian and radius r will have an arc length of r.

 So, to find the arc length in Radians, simply multiply q by r.

There are 2p radians in a full circle, i.e. 2p radians º 360 degrees.

The area of the segment is simply the area of the circle multiplied by the proportion of the whole.

In Radians thisgives us a nice formula:

To find the area of a sector, we find the area of the segment, and subtract the area of the triangle:

 

We use the formula for the area of a triangle from the formula book, area of triangle

So if we know the angle C, the area of the yellow sector can be worked out:

Sector area =

 Finally, to find the length of the chord AB, we use some simple trigonometry. If we know the angle C, we split the segment into two right-angled triangles:

We know that sin is opposite over hypotenuse, hence: