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.
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