Connecting Trigonometric Ratios to Special Right Triangles

Find the ratio of the two legs of the 60-30-90 triangle in the diagram above. (When you’re finding the ratio, use the vertical leg as the numerator and the horizontal leg as the denominator.) This ratio should hopefully look familiar, as you’re looking at the change in y over the change in x. We used to call this the slope, but with Trigonometric ratios, we’ll be calling this the Tangent of .

Find the ratio of the horizontal leg over the hypotenuse in the 60-30-90 triangle above. This ratio is referred to as the Cosine of , written as .

Find the ratio of the vertical leg over the hypotenuse in the 60-30-90 triangle above. This ratio is referred to as the Sine of , written as .