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MAIN BOARD (You must register to post) => GENERAL TOPICS  BOARD ANNOUNCEMENTS => Topic started by: There is only one God on February 10, 2013, 10:18:57 AM

sin90
I heard it is 1 but can anyone confirm please? Thanks

http://www.scribd.com/doc/36021278/Sin90Equals1Proof

http://www.scribd.com/doc/36021278/Sin90Equals1Proof
Ahhh, the old days of Calculus and Differential Equations :). I forgot most of it hehehehhe ;D.

Mathematics is my Achilles' heel, unfortunately.
"cos(θ)" is the xcomponent 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)=1
You 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.