Today in class we discussed the special triangles and how they relate to the exact values in the unit circle. We were looking at the isosceles triangle that has base angles of 45 degrees. For any isosceles triangle having base angles equal to 45 degrees the sine ratio and cosine ratio will always be the same...ie. 1/sqrt 2. If we transpose a right isosceles triangle into the unit circle, the hypotenuse will be 1 and the length of legs a and b will be the same, namely 1/sqrt 2. So the opposite side is 1/sqrt 2 and the adjacent side is 1/sqrt 2. It follows then that the sine ratio of opposite over hypotenuse is 1/sqrt2 / 1 and cosine ratio of adjacent over hypotenuse is 1/sqrt2 / 1.
So now we know that cosine 45 degrees = 1/sqrt 2 and sine 45 degrees = 1/sqrt2
Hope this answers Nick's question!
Lesson 1 Circular Functions
Lesson 2 Circular Functions
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