An Indepth Look at The Unit Circle (Part 2)

     Now, let’s do the same thing with our 45-45-90 triangle. Imagine the 45-45-90 triangle inside the Unit Circle:

    Since we know the radius is one, we can say that 1= x. By simple division, we can tell that x equals 1/.  Both of the legs of a 45-45-90 triangle are equal, so both the cosine and sine of a 45 degree angle is  .

**note** 1/ is changed to 2/ on the Unit Circle :

      

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     We don’t have to do quite so much “work” to find the cosine and sine values of a sixty degree angle. Let’s take a look at it on the Unit Circle.

     Hey look!! It’s a rotated 30-60-90 triangle!! The 30 degree and 60 degree angles have “switched places”, so to speak. Therefore, we only have to switch the cosine and sine values of a 30-60-90 triangle to find the cosine and sine values of this angle. SO: The cosine of a 60 degree angle is 1/2, and the sine is.