Chapter 4

Some trigonometry and geometry of triangles and circles

Chapter description
This chapter reminds you of what trig is for, and how it works in triangles. It also explains some of the special geometrical properties of triangles and circles, because they may be very useful to you in applications of maths to your own special subject area.
The chapter is divided into the following sections.

1. Trigonometry in right-angled triangles
   1. Why use trig ratios?
   2. Pythagoras' theorem
   3. General properties of triangles
   4. Triangles with particular shapes
   5. Congruent triangles -- what are they, and when?
   6. Matching ratios given by parallel lines
   7. Special cases -- the sin, cos and tan of 30, 45 and 60 degrees
   8. Special relations of sin, cos and tan

2. Widening the field in trigonometry
   1. The Sine rule for any triangle
   2. Another area formula for triangles
   3. The Cosine rule for any triangle

3. Circles
   1. The parts of a circle
   2. Special properties of chords and tangents of circles
   3. Special properties of angles in circles
   4. Finding and working with the equations which give circles
   5. Circles and straight lines -- the different possibilities
   6. Finding the equations of tangents to circles

4. Using radians
   1. Measuring angles in radians
   2. Finding the perimeter and area of a sector of a circle
   3. Finding the area of a segment of a circle
   4. What do we do if the angle is given in degrees?
   5. Very small angles in radians -- why we like them

5. Tidying up -- some thinking points returned to
   1. The sum of interior and exterior angles of polygons
   2. Can we draw circles round all triangles and quadrilaterals?

---

You can either look at the contents of Chapter 5
or return to basic trig for working out vector components
or you can return to my book's home page.

---