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http://www.scribd.com/doc/36021278/Sin-90-Equals-1-Proof

"cos(θ)" is the x-component of the (cos(θ),sin(θ)) and so is negative as we move from first quadrant to second quadrant.However sin(θ) is the y component and does NOT change sign. That is, if 0<θ<90, in the first quadrant, θ+90 is in the second quadrant. sin(θ+90) is still positive as is cos(θ).

sin(90)=1You can determine this by looking at the graph y=sin(x), or if you want to determine it geometrically: take a right triangle with hypotenuse of length 1. If you increase the angle theta, the opposite side increases, approaching the length of the hypotenuse (1). When theta reaches 90 degrees, you no longer have a triangle, but sin(90) is still 1.