**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

and0^{o}, 90^{o}, 180^{o}, 270^{o},.360^{o}Let's place the point

on the terminal side of the(1, 0)and the0^{o}angle. On the terminal side of the360^{o }angle,we'll place the point90^{o}. On the terminal side of the(0, 1)angle we'll place the point180^{o}, and on the terminal side of the(1, 0)angle we'll place the point270^{o}.(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", they-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 lengthto all points.1For example, using

, we findhyp = 1using point

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

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

ETC.

YOU MUST MEMORIZE THE FOLLOWING VALUES!