Tuesday, November 10, 2009

Trigonometric Ratios and Special Triangles

In this unit of trigonometry we touched upon something called radian measure, which is completely different than degree measurement. For example instead of saying 180 degrees, it is now Ï€. Therefore if Ï€ = 180 degrees then it is also safe to say 90 degrees is equaled to Ï€/2. How do "Trigonometric Ratio's" relate to Special Triangles? We learned about the special triangles in grade 11 math. There are 3 types so far that we've learned, one with two 45 degrees angles and one 90 degree angle. Another one with a 90 degree angle, 60 degree angle, and a 30 degree, angle. The last one would be the same as the 2nd special triangle but flipped around.

Sin = y/r Secant = r/y

Cos = x/r Cosine = r/x

Tan = y/x Cotangent = x/y

the "r" value is determined by the hypotenuse of the special triangle, the "x" value goes by the x axis value, meaning the adjacent side of the special triangle, the "y" value goes by the y axis which is also the opposite side. Once you use these special triangles you can determine the Sin Cos Tan of the Radian Measure you had.