A B C

Notes for Session 8, Part C

 Note 7 If you're working with a group, compare different methods other participants have come up with. Think about how these methods connect to yours.

 Note 8 These ratios have been immensely useful in many fields, such as engineering, surveying, astronomy, and architecture. In addition to the three trigonometric functions mentioned in this session (sine, cosine, and tangent), there are three additional functions not covered in this course (secant, cosecant, and cotangent).

 Note 9 In mathematics, if we have an idea that works in some particular cases, we often look for ways to extend that idea to a more general situation. For example, the definitions of the trigonometric functions on the right triangle are valid only when dealing with angles between 0° and 90° -- no other angle can appear in a right triangle! So, in order to make sense of and compute the values of trigonometric functions of any angle, we need to extend this definition. According to the extended definition, sin and cos of angle (theta) are defined to be y and x coordinates, respectively, of a point on the unit circle. (The unit circle is a circle centered at the origin of the coordinate system, with a radius equal to 1.) Notice that as we move the point P along the circle to create angles between 0° and 360°, some coordinates will be positive and some will be negative.

 Note 10 The values for sine and cosine have been calculated for many triangles. You can find them in a trigonometry table, or you can calculate them yourself using a scientific calculator.