3. Explanation of the new material (10 min.).
As already known in
the ordinate and abscissa x can be represented in the form of sine and cosine of the angle by the following formulas:
sin(a) = у,
cos(a) = х.
Substituting these values into the equation of the unit circle we have the following equality:
(sin(a))2 + (cos(a))2 =1
This equality holds for all values of the angle a. It is called the Pythagorean trigonometric identity.
From the basic trigonometric identities can be expressed by one function over another.
sin(a) = ±√(1-(cos(a))2),
cos(a) = ±√(1-(sin(a))2).
I. The ratio between the sine and cosine of the same angle.
The following figure shows the coordinate system Oxy with the image in her part of the unit semicircle ACB centered at the point A. This is part of an arc of the unit circle. The unit circle is described by the equation x2+y2=1.