Re: Would someone be so kind as to help me with a math equation?
From: Chergarj (chergarj_at_cs.comhaho)
Date: 01/09/05
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Date: 09 Jan 2005 07:14:47 GMT
GhostOfACPast@gmail.com asks on 01/08/2005:
>I am trying to convert a sin into a cos but all I could come up with
>was the half angle formula which does not give me any negatives. The
>half angle formula has the correct number but it loses the sign.
>
>Formula I tried (simplified) was
>
>x=sin(angle)
>y = sqrt(1 - x^2)
>
>At first I thought I had it because of this
>
>....Sin.........Cos......Results from the formula above
>-0.95297934 -0.30303527 0.30303528
>-0.95486454 -0.29704159 0.2970416
>-0.95671205 -0.29103617 0.29103617
>-0.95852179 -0.28501927 0.28501926
>-0.96029369 -0.27899111 0.27899109
>-0.96202767 -0.27295194 0.27295194
>-0.96372368 -0.26690199 0.26690199
>-0.96538164 -0.26084151 0.2608415
>-0.96700149 -0.25477073 0.25477072
>
>but when I tested it more I found this
>
>....Sin.........Cos......Results from the formula above
>0.05024432 -0.99873696 0.99873696
>0.04396812 -0.99903293 0.99903293
>0.03769018 -0.99928947 0.99928947
>0.03141077 -0.99950656 0.99950656
>0.0251301 -0.99968419 0.99968419
>0.01884845 -0.99982235 0.99982235
>0.01256604 -0.99992104 0.99992104
>0.00628315 -0.99998026 0.99998026
>
>Notice the digits are correct (within the tolerance of the program I
>used) but I lost their sign. Now the only numbers I know or can
>manipulate is x after the sinewave has been created.
>
>Is there a formula for a full angle as there is for a half angle?
>Thank you.
Remember where these functions come from. They are represented as triangles on
the unit circle, RIGHT triangles. You can apply pythagorean theorem. Also,
within quadrant 1, any angle has a complement; so the sine of an angle would be
the cosine of its complement. In any case, for quadrant 1 angles, (sine(x))^2
+ (cosine(x))^2 = 1. Please check a trigonometry textbook; because it will
explain this a bit more elaborately.
G C
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