POINT OF INTEREST 3
VALUES OF TRIGONOMETRIC RATIOS OF QUADRANTAL ANGLES
Copyright by Ingrid Stewart, Ph.D.  Please Send Questions and Comments to ingrid.stewart@csn.edu.

Let's derive the values of the sine, cosine, and tangent ratios of the angles with measures 0^o, 90^o, 180^o, 270^o, and 360^o.

Let's place the point (1, 0) on the terminal side of the 0^o and the 360^o angle. On the terminal side of the 90^o angle,we'll place the point (0, 1). On the terminal side of the 180^o angle we'll place the point (1, 0), and on the terminal side of the 270^o angle we'll place the point (0, 1).

We are using these points for simplicity's sake!  We could have used any other points lying on the coordinate axes.

Now, we will use the definition of the trigonometric ratios in a novel way. That is, the x-coordinates of the points will be the "side adjacent", the y-coordinates of the points will be the "side opposite", and the "hypotenuse" will be the distance from the origin to each point. In our case, this distance is of length 1 to all points.

For example, using hyp = 1, we find

 using point (1, 0)    using point (0, 1)

using point (1, 0)     using point (0, 1)

ETC.

YOU MUST MEMORIZE THE FOLLOWING VALUES!