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Title: Can anyone help me do this sin
Post by: There is only one God on February 10, 2013, 11:18:57 AM

sin90

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

Title: What?
Post by: Mujahid Saifullah on February 10, 2013, 10:28:08 PM

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

Title: Re: Can anyone help me do this sin
Post by: QuranSearchCom on February 10, 2013, 10:33:42 PM

Quote from: Mujahid Saifullah on February 10, 2013, 10:28:08 PM

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

Ahhh, the old days of Calculus and Differential Equations :).  I forgot most of it hehehehhe  ;D.

Title: Re: Can anyone help me do this sin
Post by: Mujahid Saifullah on February 10, 2013, 10:37:02 PM

Mathematics is my Achilles' heel, unfortunately.

Quote

"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).

Quote

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.